A ball thrown horizontally from the top of a building 24 m above the ground strikes the ground at the distance of 18 m from the base of the building. What was its initial velocity? (Use g = 10 m/s2.)

The nozzle's isentropic efficiency is 0.288, or 28.8%.

To determine the isentropic efficiency of the nozzle, we need to compare the actual temperature and velocity of the air leaving the nozzle to the temperature and velocity it would have if it had undergone an isentropic (reversible adiabatic) process.

We can assume that the air is an ideal gas, and we can use the following equations to relate the pressure, temperature, and specific volume of the air:

\(P1 / T1^{(\gamma)} = P2 / T2^{(\gamma)} = constant\)

\(v2 / v1 = (T1 / T2)^{(1/\gamma)\)

where P1, T1, v1 are the initial pressure, temperature, and specific volume, and P2, T2, v2 are the final pressure, temperature, and specific volume. γ is the ratio of specific heats of air and is approximately equal to 1.4.

From the problem statement, we have:

P1 = 570 kPa

T1 = 430 K

P2 = 190 kPa

T2 = 350 K

Using the first equation above, we can solve for T2 as:

\(T2 = T1 * (P2 / P1)^{(1/\gamma)\)

  \(= 430 K * (190 kPa / 570 kPa)^{(1/1.4)\)

  = 367.5 K

Now we can use the second equation to calculate the specific volume of the air at the exit:

\(v2 / v1 = (T1 / T2)^{(1/\gamma)\)

\(v2 = v1 * (T1 / T2)^{(1/\gamma)\)

  \(= R*T1 / P1 * (P2 / P1)^{(1/\gamma-1)} * (T1 / T2)^{(1/\gamma)\)

\(= 8.3145 J/(mol*K) * 430 K / (570 kPa) * (190 kPa / 570 kPa)^{(1/0.4)} * (430 K / 367.5 K)^{(1/1.4)\)

  = 0.441 m³/kg

Now, we need to assume that the exit process is isentropic and calculate the specific volume that the air would have at the exit if it had undergone an isentropic process from the initial conditions to the final pressure P2. This is given by:

\(v2s = v1 * (P1 / P2)^{(1/\gamma)\)

\(v2s = R*T1 / P1 * (P1 / P2)^{(1/\gamma-1)\)

  \(= 8.3145 J/(mol*K) * 430 K / (570 kPa) * (570 kPa / 190 kPa)^{(1/0.4-1)\)

   = 0.127 m³/kg

The isentropic efficiency of the nozzle is defined as the ratio of the actual specific volume v2 to the specific volume v2s that the air would have at the exit if it had undergone an isentropic process. Therefore, we have:

η = v2s / v2

 = 0.127 m³/kg / 0.441 m³/kg

 = 0.288

So, the isentropic efficiency of the nozzle is 0.288 or 28.8%.

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The impulse on the baseball when hit by a player's bat can be calculated using the formula for impulse, which is the product of the force applied and the time of contact. the impulse on the ball is 0.1021 Ns

In this case, since the ball is initially moving horizontally and is brought to rest in the opposite direction, the change in momentum is twice the momentum of the ball before contact. The impulse can be found by multiplying the change in momentum by the time of contact.

The initial momentum of the baseball can be calculated by multiplying its mass (0.140 kg) by its initial velocity (36.7 m/s). Since the ball comes to rest in the opposite direction, the change in momentum is equal to twice the initial momentum. The change in momentum is then multiplied by the time of contact (0.05 s) to find the impulse on the ball.

Therefore, the impulse on the ball is 0.140 kg * 36.7 m/s * 2 * 0.05 s = 0.1021 Ns.

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1) The car must be traveling at a speed of 35.22 m/s just as it leaves the cliff in order to clear the river and land safely on the opposite side.

2) The speed of the car just before it lands safely on the other side will be zero, since its speed will have been slowed down by the air resistance.

To solve this problem, we will use the equation for horizontal distance:
d = v₀t

Where,
d is the horizontal distance (58m)
vo is the initial velocity (unknown)
t is the time taken (unknown)

We can use the equation for vertical displacement:
y = y₀ + v₀t - 1/2  gt²

Where,
y is the vertical displacement (18.9m)
yo is the initial vertical displacement (19.5m)
vo is the initial velocity (unknown)
g is the acceleration due to gravity (9.8m/s²)
t is the time taken (unknown)

We will also use the equation for final velocity:
vf = v₀ - gt

Where,
vf is the final velocity (0m/s)
v₀ is the initial velocity (unknown)
g is the acceleration due to gravity (9.8 m/s²)
t is the time taken (unknown)

We can now solve the equations simultaneously to find the initial velocity required (v₀):
d = v₀t
y = y₀ + v₀t - 1/2g t²
vf = v₀ - g t

Solving these equations, we find that the initial velocity (vo) required is 35.22 m/s.

Therefore, the car must be traveling at a speed of 35.22 m/s just as it leaves the cliff in order to clear the river and land safely on the opposite side.

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Answer:

4

Explanation:

Impact Force = mv/2t

Impact force is inversely proportional to t

If m and v are constant and the only thing that changes is t, then:

0.005 s increases by a factor of 4 to 0.020 s

Therefore, impact force reduces by a factor of 4 (1/4 less than when the time of impact was 0.005 s)

Answer:

D. Twice the magnitude and the same direction as vector A.

Explanation:

When multiplying a vector by a scalar (a number), the length changes but the direction stays the same.

Therefore, vector 2A is twice the magnitude of vector A, but in the same direction as vector A.

Answer:

D

Explanation:

Here the given vector to us is 2A . Here A is a vector and 2 is a Scalar number. say when you multiply a Scalar x by vector y the magnitude becomes x *y but the direction remains same . as scalar quantities have only magnitude but no direction. Here A is multiplied by 2 so the magnitude becomes 2 times but the direction remains same.

So from the given options option D , twice the magnitude and the same direction as vector A is the correct answer.

Certainly, I'd be happy to help you. Can you please provide me with the question or problem that you need help with? Once I have that information, I'll be able to give you a clear and thorough answer with step-by-step work included.

In the meantime, I can offer you some general advice on how to approach math problems. The key to solving any math problem is to carefully read the problem and make sure you understand what it's asking you to do. Next, you'll want to identify any formulas or strategies that you can use to solve the problem. Then, you'll need to apply those formulas or strategies to the problem and carefully show your work step-by-step.

It's important to show your work not only because it helps you organize your thoughts and ensure that you're on the right track, but also because it helps your teacher or professor see your thought process and determine how you arrived at your answer. Additionally, showing your work can help you identify any mistakes you might have made and allow you to correct them before you submit your final answer.

In summary, taking the time to carefully read the problem, identify applicable formulas or strategies, and show your work step-by-step are essential to solving any math problem.

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Rounding to the nearest mile, the estimated distance you can travel is approximately 198 miles.

To estimate the distance you can travel in 4 hours and 50 minutes at an average speed of 41 miles per hour, we need to convert the time to hours.

4 hours and 50 minutes is equivalent to 4.83 hours (since 50 minutes is 50÷60 = 0.83 hours).

Now, we can calculate the distance traveled using the formula: distance = speed × time.

Distance = 41 miles/hour × 4.83 hours

Distance ≈ 198.03 miles

Rounding to the nearest mile, the estimated distance you can travel is approximately 198 miles.

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The wavelength of a wave with a frequency of 500 Hz that is traveling at a speed of 200 meters per second is 0.4 meters (m).

A wave is a disturbance that travels through space and matter, transferring energy from one location to another without actually moving any matter. Light waves, sound waves, and water waves are some examples of waves. Waves can be characterized by their amplitude, frequency, and wavelength. Wavelength is the distance between two corresponding points on a wave, such as two peaks or two troughs. It is represented by the symbol λ (lambda) and is measured in meters.

The wavelength of a wave can be calculated using the formula:

λ = v/f Where λ is the wavelength, v is the speed of the wave, and f is the frequency of the wave. Given that a wave with a frequency of 500 Hz is traveling at a speed of 200 meters per second, the wavelength can be calculated as follows:

λ = v/fλ

  = 200/500λ

  = 0.4 m

Therefore, the wavelength of the wave is 0.4 meters (m).

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Acceleration is a fundamental concept in physics that describes the rate at which the velocity of an object changes over time. It is defined as the change in velocity divided by the change in time.

Inertia is the property of an object that resists changes in its state of motion. The greater the mass of an object, the greater its inertia. Therefore, an object that has twice as much mass as another object will have twice as much inertia. gravitational acceleration, volume, and velocity are not directly proportional to an object's mass and do not necessarily double when an object's mass doubles.

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Answer:

a. Hooke's law is a principle in physics that states that the force required to extend or compress a spring or elastic material is directly proportional to the displacement of its end or deformation.

b. The formula for resistance of a wire is given by:

R = (ρL)/A

where R is resistance, ρ is resistivity, L is length, and A is cross-sectional area.

Given L = 10m, A = 0.1 mm² = 0.1 x 10^-6 m², and ρ = 50 µcm = 50 x 10^-8 Ωm, we have:

R = (50 x 10^-8 x 10) / (0.1 x 10^-6)

R = 5 Ω

Therefore, the resistance of the wire is 5 Ω.

The formula for Young's modulus is given by:

Y = F L / A ΔL

where Y is Young's modulus, F is force, L is length, A is cross-sectional area, and ΔL is the change in length.

Given F = 2 kgf = 2 x 9.81 N, L = 2 m, d = 0.64 mm = 0.64 x 10^-3 m, and ΔL = 0.60 mm = 0.60 x 10^-3 m, we have:

A = πd²/4 = π(0.64 x 10^-3)²/4 = 3.21 x 10^-7 m²

Y = (2 x 9.81 x 2) / (3.21 x 10^-7 x 0.60 x 10^-3)

Y ≈ 1.24 x 10^11 N/m²

Therefore, the Young's modulus of the wire is approximately 1.24 x 10^11 N/m².

Explanation:

Answer:

Answer

Advantages of alcohol over Mercury

(a) Freezing point of alcohol is −117∘

C and hence can record very low temperature For example in Arctic and Antarctic regions temperature may fall below −80∘

C which cannot be measured by mercury thermometer because mercury freezes at−39 ∘ C

(b) The expansion of alcohol per degree rise in temperature is much more around six times more then that of mercury and hence is more sensitive

(c) it can be coloured brightly by adding some dye in it and hence is easily detectable

Answer:gravitational, weak nuclear, electromagnetic, strong

Explanation:

The graph would look like a series of two linear slopes, one going up and one going down.

A linear slope, also known as a straight-line slope, refers to the rate of change of a linear function, which is represented by a straight line on a graph. In mathematical terms, the slope is defined as the ratio of the change in the vertical coordinate (y) to the change in the horizontal coordinate (x) between any two points on the line.

The slope of a linear function is constant throughout the line, meaning that the rate of change remains the same regardless of the position on the line. Linear slopes are used in a variety of mathematical applications, including geometry, physics, engineering, and economics, among others. They are particularly useful for modeling relationships between two variables, such as distance and time, or price and quantity.

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Answer:

Energy is the ability to do work.

Explanation: Work is just the act of displaying something by applying force.

Answer:

the height of the is 6 m.

Explanation:

Given;

potential energy of the object, P.E = 50 J

Height of fall of the object, H = 12 m

Determine the mass of the object, m

P.E = mgh

m = (P.E) / (gh)

m = (50) / (9.8 x 12)

m = 0.425 kg

Let the height of the object at 25 J = h₂

mgh₂ = 25

h₂ = (25) / (mg)

h₂ = (25) / (0.425 x 9.8)

h₂ = 6 m

Therefore, the height of the object at 25 J is 6 m.

Answer:In geometric optics, the angle of incidence is the angle between a ray incident on a surface and the line perpendicular to the surface at the point of incidence, called the normal. The ray can be formed by any wave: optical, acoustic, microwave, X-ray and so on. In the figure below, the line representing a ray makes an angle θ with the normal. The angle of incidence at which light is first totally internally reflected is known as the critical angle. The angle of reflection and angle of refraction are other angles related to beams.

Explanation:tik tok: Uh.amy07

Answer:

The angle between a ray incident on a surface and the line perpendicular to the surface at the point of incidence.

Explanation

An object's momentum is determined by multiplying its mass by its velocity. According to the rule of conservation of momentum, an isolated system's overall momentum is constant both before and after a collision.

Thus, Block A's momentum prior to the collision is caused by: Mass A * Velocity A = m * v = Momentum.

Block B's momentum prior to the collision is caused by: Momentum is defined as mass times speed, or (2m x (-v)) = -2mv.

The sum of the individual momenta of the blocks equals the total momentum prior to the collision: Total momentum before is calculated as follows: m * v - 2mv = -mv; Momentum A + Momentum B.

Thus, An object's momentum is determined by multiplying its mass by its velocity. According to the rule of conservation of momentum, an isolated system's overall momentum is constant both before and after a collision.

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The car is going at 24.6 m/s after undergoing an acceleration of 4.2 m/s2 over a distance of 450 m.

The velocity of the car initially was 9.6 m/s and the distance covered by the car is 450 m. The acceleration of the car is 4.2 m/s2. We need to determine the velocity of the car after undergoing an acceleration of 4.2 m/s2. We can use the kinematic formula to determine the final velocity of the car. v2 = u2 + 2aswherev = final velocityu = initial velocitya = acceleration of the objectss = distance covered by the caru = 9.6 m/sa = 4.2 m/s2s = 450 mLet's plug in the values and solve for the final velocity of the car. We have:v2 = u2 + 2asv2 = (9.6)2 + 2(4.2)(450)v2 = 92.16 + 3780v2 = 3872.16Taking the square root of 3872.16, we get:v = 62.22 m/s. Therefore, the car is going at 24.6 m/s after undergoing an acceleration of 4.2 m/s2 over a distance of 450 m.

Given that the velocity of the car initially was 9.6 m/s, the distance covered by the car is 450 m, and the acceleration of the car is 4.2 m/s2. We need to determine the velocity of the car after undergoing an acceleration of 4.2 m/s2.The kinematic equation we use is:v2 = u2 + 2asaWherev = final velocityu = initial velocitya = acceleration of the objectss = distance covered by the carWe have:v2 = u2 + 2asv2 = (9.6)2 + 2(4.2)(450)v2 = 92.16 + 3780v2 = 3872.16Taking the square root of 3872.16, we get:v = 62.22 m/sTherefore, the car is going at 24.6 m/s after undergoing an acceleration of 4.2 m/s2 over a distance of 450 m.

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Answer:

1 : 2 (30 : 60)

Explanation:

The rate of increase of the Earth's gravity field at latitudes 30° and 60° are in the ratio 1 : 2 because 30 : 60 simplified is 1 : 2.

If the answer does not ask for the ratio to be simplified leave its as 30 : 60.

Answer:

I believe the answer is GPS

Explanation:

Explanation:

HOPE THIS WILL HELPS YOU

Answer:

Answer B is the correct answer: "Motion of one projectile as seen from the other is a straight line."

Explanation:

Let's write the equations of motion for each projectile, using that projectile \(a\) is launched with velocity \(a\) which has components associated with the angle of launching, given in x and y coordinates as: \(a_x\,\,and\,\,a_y\).

Similarly, assume that projectile b is launched with velocity \(b\) with components due to the launching angle = \(b_x\,\,and \,\,b_y\)

then the equations of motion for the two projectiles launched at the same time (t) from the same spot (position that we assume to be at the origin of coordinates to simplify formulas) are:

\(x_a=a_x\,t\\y_a= a_y\,t-\frac{1}{2} g\,t^2\\and\\x_b=b_x\,t\\y_b= b_y\,t-\frac{1}{2} g\,t^2\)

therefore, from the frame of reference of projectile "b", the x and y position of projectile "\(a\)" would be:

\(x_{a\,b}= x_a-x_b= a_x\,t-b_x\,t=(a_x-b_x)\,t\)  which is linear in "t"

\(y_{a\,\,b}=y_a-y_b= a_y\,t-\frac{1}{2} g\,t^2-\left[ b_y\,t-\frac{1}{2} g\,t^2\right]=(a_y-b_y)\,t\) which is also linear in t.

Therefore the motion of one projectile with reference to the other is a straight line (answer B)

Notice as well that this two projectiles cannot collide because they have been launched together, and supposedly at different speeds and angles. The only way that they can share the same x-coordinate and the same y-coordinate at the same time "t" is if their velocity components are equal, which is not what we are told.

\(x_a=x_b\\a_x\,t= b_x\,t\\and\\y_a= y_b\\a_y\,t-\frac{1}{2} g\,t^2= b_y\,t-\frac{1}{2} g\,t^2\\a_y\,t=b_y\,t\\a_y=b_y\)

where the object is located

Answer:

Spiral galaxy = 1

Elliptical galaxy = 2

Irregular galaxy = 3

Explanation:

The components of the vector v are given as:

where v is the magnitude of the vector and theta is the angle.

In this case we have v=253 and theta=55.8°, plugging this values into the y component we have:

Therefore the y component is 209.25 meters.

A bus travels is north along a straight stretch of road with a constant velocity of 15m/s. Another bus travels south on the same road at the same speed. The velocity of the second bus is 15m/s.

Speed is a scalar quantity that defines how fast an object is traveling over a distance.

\(\mathbf{Speed = \dfrac{distance}{time}}\)

The velocity of an object can be defined as the shift rate in the position of an object in a specified direction over time.  

\(\mathbf{velocity = \dfrac{displacement}{time}}\)

Since the speed of the bus traveling south is equivalent to the velocity of the bus in the North, we can conclude that the velocity of the second bus is 15 m/s.

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Larger diameter, capabilities of the better gathering of light, and better resolving power are those advantages that a large diameter astronomical telescope has over a telescope of a smaller diameter.

The larger the lens or mirror which is having the diameter or aperture, the telescope will then gather more light and will be at higher resolution as the viewer has the chance to see fine in detail it can. Larger scopes also have focal lengths of longer size, which means the magnifications will be greater and the sizes of images are possible with accessibility by both the eye as well as the camera.

A larger telescope mirror is a type that allows us to view the fainter objects farther into the region of space, therefore the larger one in round nature is better. The shape does not matter just as long as it can bring light to the focus point.

Large telescopes will be having several merits over their smaller counterparts, and the concerned resolution will be as how much in detail we are able to see a celestial object is the first priority. Generally, the resolution depends mainly on two things the stability of the atmosphere as well as the aperture present in your telescope. The user can only control any one of these factors.

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So here, we use the equation:

W = ΔKE + ΔPE

Recall that: KE = 0.5mv^2, and PE = qdΔV/D

ΔKE = 0.5m(v2)^2 - 0.5m(v1)^2, where v2 and v1 are Initial and final velocity respectively.

ΔPE = PE2 - PE1

PE2 = 0, since all energy is converted to other forms, mainly kinetic energy.

PE1 = q(d1)ΔV/D

Here, W = 0.

0 = 0.5m(v2)^2 - 0.5m(v1)^2 + 0 - q(d1)ΔV/D

Simplifying a bit, and knowing that d1 = D,

0 = 0.5m((v2)^2 - (v1)^2) - qΔV

Moving qΔV to the other side,

qΔV = 0.5m((v2)^2 - (v1)^2)

Dividing by q and isolating ΔV,

ΔV = 0.5m * ((v2)^2 - (v1)^2) / q

Now, we have ΔV, which is the electric potential difference, in terms of all the variables we know.

m = 9.1 * 10^-31

v2 = 1 * 10^6

v1 = 5 * 10^6

q = 1.602 * 10^-19 (this is a well known constant)

ΔV = 0.5*9.1*10^-31 * ((5*10^6)^2 - (1*10^6)^2) / 1.602*10^-19

Solving and simplifying all of this, we get that

ΔV = 68.25 V

Answer:

Tropical region

Explanation:

because the regions near the equator are called tropical regions