Two point charges have a total electric potential energy of -24 J, and are separated by 29 cm.
If the total charge of the two charges is 45 μC, what is the charge, in μC, on the positive one?
What is the charge, in μC, on the negative one?

Answers

Answer 1

Answer:

The charge of the negative one is 13.27 microcoulombs and the positive one has a charge of 58.27 microcoulombs.

Explanation:

Electric potential energy between two point charges is derived from concept of Work, Work-Energy Theorem and Coulomb's Law and described by the following formula:

\(U_{e} = \frac{k\cdot q_{A}\cdot q_{B}}{r}\) (1)

Where:

\(U_{e}\) - Electric potential energy, measured in joules.

\(q_{A}\), \(q_{B}\) - Electric charges, measured in coulombs.

\(r\) - Distance between charges, measured in meters.

\(k\) - Coulomb's constant, measured in kilogram-cubic meters per square second-square coulomb.

If we know that \(U_{e} = -24\,J\), \(q_{A} = 45\times 10^{-6}\,C+ q_{B}\), \(k = 9\times 10^{9}\,\frac{kg\cdot m^{3}}{s^{2}\cdot C^{2}}\) and \(r = 0.29\,m\), then the electric charge is:

\(-24\,J = -\frac{\left(9\times 10^{9}\,\frac{kg\cdot m^{3}}{s^{2}\cdot C^{2}} \right)\cdot (45\times 10^{-6}\,C+q_{B})\cdot q_{B}}{0.29\,m}\)

\(-6.96 = -405000\cdot q_{B}-9\times 10^{9}\cdot q_{B}^{2}\)

\(9\times 10^{9}\cdot q_{B}^{2}+405000\cdot q_{B} -6.96 = 0\) (2)

Roots of the polynomial are found by Quadratic Formula:

\(q_{B,1} = 1.327\times 10^{-5}\,C\), \(q_{B,2} \approx -5.827\times 10^{-5}\,C\)

Only the first roots offer a solution that is physically reasonable. The charge of the negative one is 13.27 microcoulombs and the positive one has a charge of 58.27 microcoulombs.


Related Questions

950 kg
3.
If the car has 30.400 J of kinetic
energy, how fast is it moving?

Answers

m
=
950

k
g
E
=
30
,
400

J
To determine the speed of the car, we use the term for kinetic energy:

E
=
1
2
m
v
2

and we re-arrange this equation to get the speed v:

v
=

2
E
m

and we substitute:

v
=

2
(
30
,
400

J
)
950

k
g

evaluating this, we obtain the speed:

v
=
8

m
/
s

You put on sunglasses and looks at the outside view. The sky is a little dark, but the reflection from a pond is much darker. Why?

A. Pond reflection is polarized
B. The light outside has changed.
C. Sunglasses are not polarized.
D. Skylight is polarized.

Answers

When you put on sunglasses and looks at the outside view, the sky is a little dark, but the reflection from a pond is much darker because Pond reflection is polarized. Option (A) is correct.

What is polarization?

In the field of physics, polarization is referred to as a phenomena brought on by the fact that electromagnetic radiation is a wave.

Moving across space, electric and magnetic fields interact to form light. Light waves vibrate electrically and magnetically in perpendicular to one another. The magnetic field and electric field both move perpendicular to one another in different directions.

As a result, the direction of motion is perpendicular to both the plane occupied by the electric field and the plane of the magnetic field that is perpendicular to it.

These magnetic and electric vibrations can take place on a variety of planes. Unpolarized light is a type of light wave that vibrates in more than one plane. The sun, a lamp, and a tube light are all examples of unpolarized light sources.

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suppose an insect dropped off a leaf and falls to the ground. consider the forces acting on the insect when it starts to fall, when it falls at a constant speed, and when it lands. when is there a net force acting and in what direction? What force pair is there when the incest lands?

Answers

Answer:

A) When the insect starts to fall.

Assuming that the little insect can not do anything (he/she does not have wings or anything like that) the only force acting on the insect will be:

Gravitational force: Is the force that pulls down the insect.

Air resistance: As the insect starts to move, the air will try to oppose to that motion.

B) When the insect falls at a constant speed.

This will happen when the air resistance equals in magnitude (but in opposite direction) the gravitational force.

Now the net force is zero, so the insect is not accelerated anymore, which means that the insect moves at a constant speed.

And the fact that the net force is zero does not mean that the gravitational force and the air resistance are "not acting" on the insect, this means that those forces are not having any effect in the dynamics of the insect's motion.

C) When it lands.

When the insect lands, there is a new force that appears, the normal force of the ground that opposes to the movement of the insect through it.

As the insect comes to stop (because he hits the ground) the air resistance does not longer act on it, so now the normal force of the ground is equal in magnitude (but in opposite direction) to the gravitational force, then the net force is zero.

D) When is there a net force acting and in what direction?

The only time that is a net force acting, is when the insect starts to fall, where the gravitational force is accelerating the insect downwards.

E) What force pair is there when the insect lands?

The force pair is the gravitational force, and the reaction, the normal force of the ground.

Push a box across a table with a force of 5 newtons and the box moves
0.5 meters. How much work has been accomplished?
If you do

Answers

Answer:

2.5J

Explanation:

Work done = Force x Distance

= 0.5 x 5

= 2.5J

The work done that should be accomplished should be 2.5 J.

Calculation of the work done:

Since the force is 5 newtons

The box moves 0.5 meters

So here the work done should be

= Force x Distance

= 0.5 x 5

= 2.5J

here we basically multiply the force with the distance so that the work done should be determined.

hence, The work done that should be accomplished should be 2.5 J.

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2. Gerard is riding his bicycle directly east. His maximum
instantaneous velocity was 8 meters per second and his
minimum instantaneous velocity was 0 meters per second. He
covered 7.20 kilometers in 20.0 minutes. What is his average
velocity for the ride?

Answers

Gerard's average velocity for the ride is 6 meters per second.

To find Gerard's average velocity for the ride, we can use the formula:

Average velocity = Total displacement / Total time

First, we need to convert the distance traveled from kilometers to meters:

7.20 kilometers * 1000 = 7200 meters

Next, we convert the time from minutes to seconds:

20.0 minutes * 60 = 1200 seconds

Now, we can calculate the total displacement by subtracting the initial position from the final position. Since Gerard is riding directly east, there is no change in the east-west direction, so the displacement is equal to the distance traveled:

Total displacement = 7200 meters

Finally, we substitute the values into the average velocity formula:

Average velocity = 7200 meters / 1200 seconds

Average velocity = 6 meters per second

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If you travel from Tucson to Argentina, you will see some different constellations in the night sky. true or false

Answers

Answer:

its true!!

Explanation: have a nice day !!

If velocity is 0.2m/s, what is the kinetic energy?

Answers

\( \huge\boxed{♧ \: \mathfrak{ \underline{Answer} \: ♧}}\)

we know,

\( \boxed{kinetic \: \: energy = \frac{1}{2} m {v}^{2} }\)

So,

\(\longmapsto \dfrac{1}{2} \times 10 \times 0.2 \times 0.2\)

\(\longmapsto0.2 \: joules\)

A box with a mass of 6.25kg is sliding along a horizontal surface at constant velocity. It is pulled by a horizontal force, and the coefficient of kinetic friction between the box and the surface is 0.431. What is the work done, in joules, by the force of friction on the box as the box moves a distance of 0.497m?

Answers

The work done, by the force of friction on the box as the box moves a distance is 13.12 J.

What is work done by the force of friction?

The work done by force of friction is calculated from the product of force of friction and distance through which the object travelled and it is given as;

W = Fₙd

where;

Fₙ is the force of frictiond is the distance travelled by the object

W = μmg x d

Where;

μ is coefficient of kinetic frictionm is mass of the boxg is acceleration due to gravityd is the distance travelled

W = 0.431 x 6.25 x 9.8 x 0.497

W = 13.12 J

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An environmentally conscious physics student 250 N
mows her lawn with a push mower, exerting
a force of 250 N along the handle as shown. 40°
How much force is actually being used to push
the mower along the grou

Answers

The force actually being used to push the mower along the ground is 191 N.

When the physics student exerts a force of 250 N along the handle of the push mower, it's important to consider the components of this force that contribute to the actual force used to push the mower along the ground.

To determine the force used to push the mower along the ground, we need to find the horizontal component of the applied force. The angle of 40° indicates that the applied force can be broken down into two components: the horizontal component and the vertical component. The vertical component of the force is perpendicular to the direction of motion and does not contribute to pushing the mower forward.

To find the horizontal component, we can use trigonometry. The horizontal component is given by the formula:

Horizontal component = Applied force * cos(angle)

Plugging in the values, we get:

Horizontal component = 250 N * cos(40°)

Calculating this value, we find that the horizontal component of the applied force is approximately 191 N.

Therefore, the force actually being used to push the mower along the ground is 191 N. This is the component of the applied force that contributes to the forward motion of the mower, while the remaining vertical component is directed perpendicular to the ground and does not assist in pushing the mower forward.

By exerting a force of 250 N along the handle at a 40° angle, the student effectively applies 191 N of force to push the mower along the ground, ensuring efficient use of their effort while considering the environmental impact.

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A falling object with a mass of 2.55 kg encounters 4.0 N of air resistance. What is the acceleration of the object? (Choose up to be the positive direction, and remember the definition of weight).

Question 9 options:

a)

-21 N


b)

-241.0 m/s2


c)

-21.0 m/s2


d)

-8.2 m/s2


e)

8.2 m/s2

Answers

The acceleration of the falling obeject of mass 2.55 kg is  -8.2 m/s². And the right option is d) -8.2 m/s².

What is acceleration?

This can be defined as the rate of change of velocity.

To calculate the acceleration of the object, we use the formula below.

Formula:

a = (R-mg)/m............. Equation 1

Where:

a = Acceleration of the objectm = Mass of the objectR = Air resistanceg = Acceleration due to gravity.

Note: Taking forces acting upward to be positve and downward force to be negatove,

From the question,

Given:

R = 4 Nm = 2.55 kgg = 9.8 m/s²

Substitute these values into equation 2

a = [4-(2.55×9.8)]/2.55a = -20.99/2.55a = -8.2 m/s²

Hence, The acceleration of the object is -8.2 m/s².

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HALP I NEED THE ANSWER!!!! Move on to electric force. Blow up the two balloons and knot them. Then tie a thread onto each balloon. Suspend the two balloons using tape so that they’re about six inches apart, and check that they don’t move or interact. Rub both balloons with wool or fur. If wool or fur is not available, rub the balloons on your hair. Do they attract or repel (push away) each other?

Answers

Answer:

Attract

Explanation:

The balloons attract each other due to electrons.

Hope this helps :)

What is Sound? How can you produce a loud sound?​

Answers

Answer:

Sound is a type of energy made by a vibrating object.

Explanation:

You can create sounds by:

- A string plucked with force has greater amplitude

- A vibrating guitar string makes the sound, if you pluck the string harder, it will make a louder sound.

i need help i was at school in high school because i am in 9 grade a kid name summer ebby is makeing me mad she never stops talking she makes me mad and upset she says like can i ask a question or can i ask you she never stops talking what i should do if a student do not stops talking ​

Answers

Just continue to ignore her. If she continues to do it, tell a teacher or someone and they will figure it out.

While Kepler supported the Copernican model of the universe Kepler concluded the following

A the circular orbits of the copernican model weren’t correct paths of planets were elliptical

B all other bodies in the universe move around the earth in circular paths

C all other bodies in the universe move around the moon in triangular paths

D the circular orbits of the Copernican model weren’t correct paths of planets were rectangular

Answers

Kepler came to the conclusion that the orbit of earth around the sub is elliptical not circular so it should be A. Good luck and hope this helps

Answer:

Explanation: because Keller concluded that the circular obits of the Copernican model weren't correct paths of planets were elleptical

Franklin is observing an object that is taking in energy at the same rate it is giving energy off.
What is true about this object?

Answers

If an object is taking in energy at the same rate it is giving energy off, it implies that the object is in a state of energy equilibrium or balance.

What is true about this object?

In other words, the amount of energy it absorbs or receives is equal to the amount of energy it emits or gives off. This suggests that the object is neither gaining nor losing energy over time.

Based on this information, it can be inferred that the object is in a stable condition regarding its energy exchange. It is maintaining a steady state without any net gain or loss of energy. This state of equilibrium could be due to various factors such as the object being in thermal equilibrium with its surroundings or being subject to a balanced energy input and output mechanism.

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The following statements explain how the activity in Earth’s layers results in changes on the surface. Which of these statements is false because it contains a misconception?

A: At subduction zones, parts of the lithosphere are being melted, forming magma.

B: Volcanic islands form over a split in Earth’s lithosphere, where the hot, liquid metallic core is closest to the surface.

C: As the hot, convecting region in the mantle moves, the lithosphere above it moves in the same direction as the convection current below.

D: The height of a volcanic island declines due to loss of heat and pressure as the lithosphere moves away from a hot spot in the mantle below.

Answers

C: As the hot, convecting region in the mantle moves, the lithosphere above it moves in the same direction as the convection current below.

i'm not sure

The stopping distances associated with slower speeds approximate the forward visibilities provided by low beam lights. However, the illumination provided by low beam lights, about 150 feet, does not provide enough visibility in high speed driving situations where stopping distances are two or more times longer than the illumination distance provided by low beam lights. a. True b. False

Answers

Answer:

a. True

Explanation:

Illumination distance is the distance, up to which the light of the vehicle can reach. Hence, it is a maximum distance from the, that driver can see.

Stopping distance is the minimum distance required by the car to stop after brakes are applied.

So, in order to avoid any accident the illumination distance must be greater than the stopping distance. So, the driver can stop the vehicle in time, when he sees something in front of it.

Since, the stopping distance in this case is two or three times longer than illumination distance. Therefore, low beam light does not provide enough visibility in high speed driving situations.

Hence, the correct option is:

a. True

3. A cylindrical steel drum is tipped over and rolled along the floor of a ware house. If the drum has radius of 0.40m and makes on complete turns in every 8.0 s, how long does it take to roll the drum 36m?​

Answers

It takes approximately 9.05 seconds to roll the drum a distance of 36 meters.

What is circumference of a circle?

We can use the formula for the circumference of a circle:

Circumference = 2 * π * radius

Given:

Radius (r) = 0.40 m

Circumference (C) = 2 * π * 0.40 m

We must figure out how many full rotations the drum makes to go 36 meters in order to calculate how long it takes to roll the drum. Since we are aware of the circumference, we can determine the number of full turns as follows:

Number of turns = Distance / Circumference

Given:

Distance = 36 m

Number of turns = 36 m / (2 * π * 0.40 m)

Now that we know how many turns there are, we can calculate the time by multiplying that number by the length of a turn, which is given as 8.0 seconds:

Time = Number of turns * Time per turn

Time = (36 m / (2 * π * 0.40 m)) * 8.0 s

By substituting the values into the equation, we can calculate the time:

Time = (36 / (2 * 3.14159 * 0.40)) * 8.0 s

Time ≈ 9.05 s

So, it takes approximately 9.05 seconds to roll the drum a distance of 36 meters.

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The NEC states the resistance of 4/0 coated
copper conductors is 0.0626 ohms per 1000
feet. What would be the total resistance of the
three 4/0 conductors installed in parallel, if the
total length for each of the three conductors is
323 feet?

Answers

Answer:

The resistance of 4/0 coated copper conductors is given as 0.0626 ohms per 1000 feet. To find the total resistance of the three 4/0 conductors installed in parallel, we can use the formula for combining resistances in parallel.

Since the total length for each of the three conductors is 323 feet, the resistance of each conductor can be calculated as follows:

Resistance of one conductor = (0.0626 ohms / 1000 feet) * 323 feet

To find the total resistance when the conductors are in parallel, we use the formula:

1/Total Resistance = 1/Resistance of Conductor 1 + 1/Resistance of Conductor 2 + 1/Resistance of Conductor 3

Total Resistance = 1 / (1/Resistance of Conductor 1 + 1/Resistance of Conductor 2 + 1/Resistance of Conductor 3)

Substituting the values, we get:

Total Resistance = 1 / (1/((0.0626 ohms / 1000 feet) * 323 feet) + 1/((0.0626 ohms / 1000 feet) * 323 feet) + 1/((0.0626 ohms / 1000 feet) * 323 feet))

Simplifying the expression will give us the total resistance of the three 4/0 conductors installed in parallel.

A 52.07kg cannon has a recoil velocity of 7.75m/s after it launches a 9.06kg projectile horizontally. The cannon ball hits a 26.28kg target (haystack) several meters away. It takes only 0.32 seconds for the cannon ball to pass through the target breaking it into two segments of equal mass one launching at 27.89 degrees off center in the x, the other 39.62 degrees off center in the y. Assume the cannon ball continues in a true horizontal trajectory.what is the momentum of the cannon ball before the collision with the haystack?

Answers

Given data:

* The mass of the cannon is 52.07 kg.

* The recoil velocity of the cannon is 7.75 m/s.

* The mass of the cannon ball is 9.06 kg.

Solution:

By the law of conservation of the momentum,

The momentum of the cannon ball before the collision is the same as the momentum of the cannon ball from the cannon.

The momentum of the cannon ball from the cannon is,

\(p=mv\)

where m is the mass of the cannon and v is the recoil velocity of the cannon,

Substituting the known values,

\(\begin{gathered} p=52.07\times7.75 \\ p=403.54kgms^{-1} \end{gathered}\)

Thus, the momentum of the cannon ball before the collision is 403.54 kgm/s.

You wear lead to protect you from ____.
gamma rays
infrared rays
x-rays
microwaves

Answers

Answer: X-rays

Explanation: Lead is used for shielding in x-ray machines. Lead is very thick and blocks x-rays.

Answer:

x-rays

Explanation:

lead is a metal so we all know that heat goes through metal, so that is no on the microwaves and infrared rays, and gamma has such a high frequency that it moves straight through any material that isn't tempered with

A 0.47-kg block is hung from and stretches a spring that is attached to the ceiling. A second block is attached to the first one, and the amount that the spring stretches from its unstretched length triples. What is the mass of the second block

Answers

Answer:

The mass of the second block is 0.94 kg

Explanation:

Given;

mass of the first block, m₁ = 0.47 kg

let the mass of the first block and second block = m₂

According to Hook's law;

F = kx

where;

F is the applied load (force)

k is the elastic constant

x is the extension of the elastic material

According to Newton's law of motion;

F = ma = mg

Thus,

mg = kx

\(k = \frac{mg}{x} \\\\\frac{m_1g}{x_1} = \frac{m_2g}{x_2} \\\\But, x_2 \ is \ triple \ of \ x_1,\\x_2 = 3x_1\\\\\frac{m_1g}{x_1} = \frac{m_2g}{3x_1}\\\\\frac{m_1}{x_1} = \frac{m_2}{3x_1}\\\\Substitute \ in \ the \ value \ of \ m_1\\\\\frac{0.47}{x_1} = \frac{m_2}{3x_1}\\\\\frac{0.47}{1} = \frac{m_2}{3}\\\\m_2 = 3 *0.47\\\\m_2 = 1.41 \ kg\)

mass of the second block alone = 1.41 - 0.47 = 0.94 kg

Therefore, the mass of the second block is 0.94 kg

write down the value of

920 kg in g

Answers

Answer:

920000

Explanation:

Each kg contains 1,000 grams

you have water in two buckets of equal height.Your friend asked you which bucket contains the moat water.Now how did you find out .write short answer​

Answers

To determine which bucket contains more water, I would pour the water from one bucket into the other until they are both at the same level. Then, I would compare the amount of water left in each bucket. The bucket with more water remaining is the one that originally had more water.

a lady drove her car northwest for a distance of 10km, then east for 40km and then south for 60km. calculate the overall displacement of the car from the starting point.​

Answers

Answer:

Explanation:

The overall displacement can be found using the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the overall displacement) is equal to the sum of the squares of the other two sides.

Let's call the displacement in the northwest direction "x" and the displacement in the east direction "y". The overall displacement can be found using the equation:

√(x^2 + y^2) = √((-10)^2 + (40)^2 + (-60)^2) = √(1600 + 1600 + 3600) = √(7000) = 84.85 km

So the overall displacement of the car from the starting point is approximately 84.85 km.

A 50-kg ice skater turns a bend at 7 m/sec. If the radius of the curve is 5 m, what is the centripetal force in Newtons provided by the friction between the blade of the skate and the ice?

Answers

The centripetal force in Newtons provided by the friction between the blade of the skate and the ice is 490 N

How do i determine the centripetal force?

The following data were obtained from the question:

Mass of ice skater (m) = 50 KgVelocity (v) = 7 m/sRadius (r) = 5 metersCentripetal force (F) =?

The centripetal force can be obtained as illustrated below:

F = mv²/r

= (50 × 7²) / 5

= (50 × 49) / 5

= 2450 / 5

= 490 N

Thus, we can concluded that the centripetal force is 490 N

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A 0.75 kg model car is moving west at a speed of 9.0 m/s when it collides head-on with a 2.00 kg model truck that is traveling east at a speed of 10.0 m/s. After the collision, the 0.75 kg model car is now moving east at 11 m/s. What is the speed and direction of the model truck after the collision?

Answers

Answer:

  2.5 m/s east

Explanation:

Let east be the positive direction for velocity.

The change in momentum of the 0.75 kg model car is ...

  m1·v2 -m1·v1 = (0.75 kg)(11 m/s) -(0.75 kg)(-9 m/s)

  = (0.75 kg)(20 m/s) = 15 kg·m/s

The change in momentum of the 2.0 kg model car is the opposite of this, so the total change in momentum is zero.

  m2·v2 -m2·v1 = (2 kg)(v2 m/s) -(2 kg)(10 m/s) = 2(v2 -10) kg·m/s

The required relation is ...

  15 kg·m/s = -2(v2 -10) kg·m/s

  -7.5 = v2 -10 . . . . divide by -2

  2.5 = v2 . . . . . . . add 10

The velocity of the model truck after the collision is 2.5 m/s east.

HELP!!! A sprinter has a speed of 10m/s and a mass of 80kg. What is the sprinter’s kinetic energy (in joules)?

Answers

Answer:

4000j

Explanation:

0.5 × 10^2 × 80 = 4kJ = 4000Joules

A cannonball is fired horizontally from the top of a cliff. The cannon is at height H = 55.5 m above ground level, and the ball is fired with initial horizontal speed . The projectile lands at a distance D = 140 m from the cliff. Assume that the cannon is fired at time t = 0 and that the cannonball hits the ground at time . a. What is the value of ? b. What is the y position of the cannonball at the time c. Find the initial speed of the projectile.

Answers

a) The value of t u = 140/t`b.

b) The y position of the cannonball at the time t is  55.5 mc.

c) The initial speed of the projectile is 52.4 m/s.

Given that a cannonball is fired horizontally from the top of a cliff. The cannon is at height H = 55.5 m above ground level, and the ball is fired with initial horizontal speed u. The projectile lands at a distance D = 140 m from the cliff. Assume that the cannon is fired at time t = 0 and that the cannonball hits the ground at time t.Now,We have to find the value of t, y position of the cannonball at the time t and the initial speed of the projectile.

a. To find the value of t:Here, we have to use the formula of distance

i.e.,S = ut + (1/2)gt², Where S = 140 m, u = u and g = 9.8 m/s².Hence,140 = u×t ………..(1)We know that, time taken by the cannonball to hit the ground can be calculated as,`(2H)/g`

Since the height of the cannon from the ground is 55.5m, the total height of the cannonball from the ground is

(2H) = 2 × 55.5

= 111 m`2H/g

= 111/9.8`

= 11.32653 s

From equation (1),u×t = 140u = 140/t

Therefore, `u = 140/t`b.

b)To find the y position of the cannonball at the time t:

Here, we have to use the formula of height i.e.,y = u×t – (1/2)gt²,

Where, y = height of the cannonball at time t, u = 140/t, t = time taken by the cannonball to hit the ground and g = 9.8 m/s².

We have already calculated the time taken by the cannonball to hit the ground in the previous step.`

y = 140 - (1/2) × 9.8 × t²`

On substituting the value of t as `t = 11.32653`,

we get,y = 140 - (1/2) × 9.8 × (11.32653)²= 55.5 mc.

c)  To find the initial speed of the projectile:

To calculate the initial speed of the projectile, we need to use the formula of range of projectile

.i.e.,R = u²sin2θ/g

Where R = 140 m, g = 9.8 m/s², θ = 0° (horizontal)

u² = R × g/sin2θ

   = 140 × 9.8/sin0°  

   = 2744m²/s²u  

   = \(\sqrt(2744m^2/s^2)\)

   = 52.4 m/s

Hence, the initial speed of the projectile is 52.4 m/s.

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Heather and Jerry are standing on a bridge 46 m
above a river. Heather throws a rock straight down with a speed of 14 m/s
. Jerry, at exactly the same instant of time, throws a rock straight up with the same speed. Ignore air resistance. How much time elapses between the first splash and the second splash?

Answers

The time elapsed between the first splash and the second splash is approximately 0.69 seconds.

To calculate this, we consider the motion of two rocks thrown simultaneously from a bridge. Heather throws a rock straight down with a speed of 14 m/s, while Jerry throws a rock straight up with the same speed.

We use the equation for displacement in uniformly accelerated motion: s = ut + (1/2)at^2.

For Heather's rock, which is thrown downwards, the initial velocity (u) is positive and the acceleration (a) due to gravity is negative (-9.8 m/s^2). The displacement (s) is the height of the bridge (46 m).

Solving the equation, we find two possible values for the time (t): t ≈ -4.91 s and t ≈ 1.91 s.

Since time cannot be negative in this context, we discard the negative value and consider t ≈ 1.91 s as the time it takes for Heather's rock to hit the water.

For Jerry's rock, thrown upwards, we use the same equation with the same initial velocity and acceleration. The displacement is also the height of the bridge, but negative.

Solving the equation, we find t ≈ -5.68 s and t ≈ 1.22 s. Again, we discard the negative value and consider t ≈ 1.22 s as the time it takes for Jerry's rock to reach its maximum height before falling back down.

To find the time difference between the first and second splash, we subtract t ≈ 1.91 s (Heather's rock) from t ≈ 1.22 s (Jerry's rock). This gives us a time difference of approximately 0.69 seconds.

Therefore, the time elapsed between the first splash and the second splash is approximately 0.69 seconds.

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