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Chapter 2: Problem 19

The terminal speed of a ping-pong ball is about \(20 \mathrm{mph}\). From the top of a building a ping-pong ball is thrown downward with an initial speed of \(50 \mathrm{mph}\). Describe what happens to the ball's speed as it moves downward from the moment it is thrown to the moment when it hits the ground.

Short Answer

Expert verified
Question: Describe the changes in a ping-pong ball's speed when it is thrown downward from a building with an initial speed of 50 mph and a terminal speed of 20 mph. Answer: When the ping-pong ball is thrown downward with an initial speed of 50 mph, its speed decreases due to air resistance. Eventually, the air resistance becomes equal in magnitude to the gravitational force, causing the ball to reach its terminal speed of 20 mph. From that point onward, the ball moves downward at a constant speed of 20 mph until it reaches the ground.

Step by step solution

01

Define terminal speed

Terminal speed is the constant speed that a freely falling object eventually reaches when the resistance of the medium through which it is falling (in this case, air) prevents further acceleration. In this exercise, it is given that the terminal speed of a ping-pong ball is about \(20 \mathrm{mph}\).
02

Describe the initial motion of the ping-pong ball

When the ping-pong ball is thrown downward with an initial speed of \(50 \mathrm{mph}\), it starts moving in a downward direction with an acceleration due to gravity (approximately \(-9.8\,\text{m/s}^2\)). However, as the ball moves downward, air resistance acts opposite to the direction of motion, slowing down its speed.
03

Explain when the ball reaches terminal speed

As the ping-pong ball travels downward, the air resistance acting on the ball continues to increase. When the air resistance becomes equal in magnitude to the gravitational force acting on the ball, the ball no longer accelerates and reaches its terminal speed. In this case, the terminal speed is \(20 \mathrm{mph}\).
04

Describe the motion of the ball after reaching terminal speed

Once the ping-pong ball has reached its terminal speed of \(20 \mathrm{mph}\), it will continue to move downward at this constant speed (assuming no other forces act on the ball). The air resistance and gravitational force are balanced, so the ball does not experience any net force or acceleration.
05

Summarize the changes in the ball's speed

Initially, the ping-pong ball is thrown downward with a speed of \(50 \mathrm{mph}\). As it moves downward, its speed decreases due to air resistance. Once the air resistance becomes equal in magnitude to the gravitational force, the ball reaches its terminal speed of \(20 \mathrm{mph}\). From this point onward, the ball moves downward at a constant speed of \(20 \mathrm{mph}\) until it hits the ground.

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