Question

Jason kicked a soccer ball and the that was lying on the ground. It was in the air for 3 seconds before it hit the ground again. While the ball was in the air it reached a maximum of 30ft. The height of the ball while in the is a function of time.

Answer 1

The ball was in the air for approximately 1.91 seconds.

Step-by-step explanation:

To calculate the maximum height reached by the soccer ball, we can use the concepts of projectile motion. The height of the ball while in the air is determined by the equation:

h(t) = h0 + v0yt - 0.5gt2

where h(t) is the height of the ball at time t, h0 is the initial height (0 ft in this case), v0y is the initial vertical component of velocity (0 ft/s in this case), g is the acceleration due to gravity (32 ft/s2), and t is the time.

Since the maximum height of the ball is 30 ft, we can set the equation equal to 30 and solve for t:

30 = 0 + 0t - 16t2

16t2 = 30

t2 = 30/16

t = √(30/16)

t ≈ 1.91 seconds

Therefore, the ball was in the air for approximately 1.91 seconds.