Question

A ball is thrown vertically upward, which is the positive direction. A little later it returns to its point of release. The ball is in the air for a total time of 7.2 s. What is its initial velocity?

Answer 1

The initial vertical velocity of the ball that was thrown straight up into the air and returned in 7.2 seconds is 35.28 meters per second upward.

Step-by-step explanation:

The student is asking about the initial vertical velocity of a ball thrown straight up into the air. Given the total time the ball is in the air is 7.2 seconds, we can use this information to find the initial velocity, assuming acceleration due to gravity is -9.8 m/s2.

Since the ball takes 7.2 seconds for the entire trip, it takes half that time, or 3.6 seconds, to reach the peak of its trajectory. At the top of its flight, the ball's velocity is 0 m/s. Using the kinematic equation v = u + at, we can calculate the initial velocity (u) as follows:

v = u + at
0 = u + (-9.8 m/s2)(3.6 s)
u = (9.8 m/s2)(3.6 s)
u = 35.28 m/s

The initial velocity of the ball is 35.28 meters per second upward.