Question

A soccer ball is kicked straight up in the air with an initial velocity of 17 m/s and rises to a height of 14.7 m before beginning to fall back down. How long (in total) is the soccer ball in the air?

A. 1.7 seconds
B. 7.0 seconds
C. 3.5 seconds
D. 1.2 seconds

Answer 1

The soccer ball is in the air for approximately 3.5 seconds.

Step-by-step explanation:

To find the total time the soccer ball is in the air, we need to consider the time it takes for the ball to rise to its maximum height and then fall back down.

First, we can use the kinematic equation vf = vi + at to find the time it takes for the ball to reach its maximum height. The initial velocity (vi) is 17 m/s, the final velocity (vf) is 0 m/s (at the top of the trajectory), and the acceleration (a) is -9.8 m/s² (assuming the positive direction is upwards and gravity is acting downwards).

Next, we can use the same equation to find the time it takes for the ball to fall back down. The initial velocity is 0 m/s (at the top of the trajectory) and the final velocity is -17 m/s (going back down). Again, the acceleration is -9.8 m/s².

Adding the two times together gives us the total time the soccer ball is in the air.

Using these calculations, the soccer ball is in the air for approximately 3.5 seconds. Therefore, the correct answer is C. 3.5 seconds.