/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 51 A tennis player tosses a tennis ... [FREE SOLUTION] | 91影视

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Chapter 2: Problem 51

A tennis player tosses a tennis ball straight up and then catches it after \(2.00 \mathrm{~s}\) at the same height as the point of release. (a) What is the acceleration of the ball while it is in flight? (b) What is the velocity of the ball when it reaches its maximum height? Find (c) the initial velocity of the ball and (d) the maximum height it reaches.

Short Answer

Expert verified
The acceleration of the ball while it is in flight is \( -9.8 \mathrm{~m/s^2}\), the velocity of the ball when it reaches its maximum height is \(0 \mathrm{~m/s}\), the initial velocity of the ball is \(9.8 \mathrm{~m/s}\), and the maximum height it reaches is \(4.9 \mathrm{~m}\)

Step by step solution

01

Indentify the acceleration of the ball while in flight

As the ball is in flight and there's no other force acting on it except gravity, the acceleration of the ball will be equal to the acceleration due to gravity. Gravity always acts downwards, therefore the acceleration of the ball in flight is \(a = -9.8 \mathrm{~m/s^2}\)
02

Find the velocity of the ball when it reaches its maximum height

At the maximum height, the velocity of the ball becomes zero for an instant- just before it starts to fall back down, after being thrown up. This is due to the fact that the ball decelerates under the pull of gravity, ceasing upward motion at the highest point. So, the velocity of the ball at its maximum height is \(v = 0 \mathrm{~m/s}\)
03

Calculate the initial velocity of the ball

We can use the equation of motion \(v = u + at\) to calculate the initial velocity (u), where v is the final velocity, a is acceleration and t is time. At maximum height, final velocity is 0, acceleration is \( -9.8 \mathrm{~m/s^2}\), and the time for upward journey would be half the total time, because the upward journey time equals the downward journey time under symmetric conditions. Thus, \(t = 2.00 \mathrm{~s} \div 2 = 1.00 \mathrm{~s}\). So, substituting these values into the equation gives \(0 = u - 9.8 \times 1.00\), which gives \(u = 9.8 \mathrm{~m/s}\)
04

Compute the maximum height the ball reaches

We can solve for the maximum height using the equation of motion \(s = ut + 0.5at^2\), where s is the displacement (maximum height in this case), u is the initial velocity, a is the acceleration, and t is the time. Substituting into that equation: \(s = 9.8 \times 1.00 + 0.5 \times -9.8 \times (1.00)^2 = 4.9 \mathrm{~m}\)

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Most popular questions from this chapter

A speedboat moving at \(30.0 \mathrm{~m} / \mathrm{s}\) approaches a no-wake buoy marker \(100 \mathrm{~m}\) ahead. The pilot slows the boat with a constant acceleration of \(-3.50 \mathrm{~m} / \mathrm{s}^{2}\) by reducing the throttle. (a) How long does it take the boat to reach the buoy? (b) What is the velocity of the boat when it reaches the buoy?

A train is traveling down a straight track at \(20 \mathrm{~m} / \mathrm{s}\) when the engineer applies the brakes, resulting in an acceleration of \(-1.0 \mathrm{~m} / \mathrm{s}^{2}\) as long as the train is in motion. How far does the train move during a 40 -s time interval starting at the instant the brakes are applied?

A car starts from rest and travels for \(t_{1}\) seconds with a uniform acceleration \(a_{1} .\) The driver then applies the brakes, causing a uniform acceleration \(a_{2}\). If the brakes are applied for \(t_{2}\) seconds, (a) how fast is the cas going just before the beginning of the braking period: (b) How far does the car go before the driver begins to brake? (c) Using the answers to parts (a) and (b) as the initial velocity and position for the motion of the ca during braking, what total distance does the car travel Answers are in terms of the variables \(a_{1}, a_{2}, t_{1}\), and \(t_{2}\).

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