Questions: A ball is equipped with a speedometer and launched straight upward. The speedometer reading two seconds after launch is shown at the right; the ball is moving upward. At what approximate times would the ball be moving downward and display the following speedometer readings?

A ball is equipped with a speedometer and launched straight upward. The speedometer reading two seconds after launch is shown at the right; the ball is moving upward. At what approximate times would the ball be moving downward and display the following speedometer readings?

Transcript text: A ball is equipped with a speedometer and launched straight upward. The speedometer reading two seconds after launch is shown at the right; the ball is moving upward. At what approximate times would the ball be moving downward and display the following speedometer readings?

Solution

Solution Steps

Step 1: Analyze the initial condition

The initial speed of the ball is 40 m/s at t=2 seconds. It's moving upwards, against the acceleration due to gravity.

Step 2: Determine the time to reach maximum height

The acceleration due to gravity is approximately -9.8 m/s². Since the ball is decelerating at this rate, we can find the time it takes for the upward velocity to become 0 (maximum height). The change in velocity is 40 m/s (from 40 m/s to 0 m/s). Time = change in velocity / acceleration = 40 m/s / 9.8 m/s² ≈ 4.1 seconds. This is the time it takes _from the 2-second mark_. So, the ball reaches maximum height at approximately 2 s + 4.1 s = 6.1 seconds.

Step 3: Calculate the time for the first speedometer reading

The first speedometer shows a reading of 20 m/s downwards. Since the motion is symmetrical, the ball will have a velocity of 20 m/s downwards 4.1 seconds _after_ reaching its maximum height. Thus, the time will be approximately 6.1 s + 4.1 s = 10.2 seconds.

Step 4: Calculate the time for the second speedometer reading

The second speedometer shows 20 m/s upwards. We already determined this speed upwards occurs at t=2s.