Question

A football is kicked vertically upward from the ground and a student gazing out of a window sees it coming passed him at 16ft/sec. The window is 30ft above the ground.

a. How high does the ball go above the ground?

b. How long does it take to go from a height of 30ft to the highest point?

Answer 1

a and b) We know that the velocity upwards is determined by

$V=V_0-gt \\ \implies 0 \,ft/s=16\,ft/s -(32.2\,ft/s^2)t \\ \implies t=\frac{16\,ft/s}{32.2\,ft/s^2}=0.497\,s$

that result allow us to calculate the height by considering that the initial velocity occurs when the height reached is 30 ft. The final height is described by

$h=h_0 + V_0t -\frac{gt^2}{2} \\ h=30\,ft+(0.497\,s)(16\,ft/s -\frac{(32.2\,ft/s^2)(0.497\,s)}{2}) \\ h=33.98\,ft$

In conclusion, the maximum height reached from the bottom is 33.98 ft while it takes 0.497 s for the ball to reach the maximum height.

Reference:

Young, H. D., Freedman, R. A., & Ford, A. L. (2006). Sears and Zemansky's university physics (Vol. 1). Pearson education.