# Math Help - Velocity problem

1. ## Velocity problem

A ball is hit straight up from a height of 4 ft with an initial velocity of 65 ft/sec. Find the maximum height of the ball and the number of seconds to reach that height.

Thank you in advance for any help!

2. Initial velocity of ball $u = 65 \;\;ft/s$

acceleration due to gravity, $g = -9.81 \;\;m/s^2$(acting downwards)

at maximum height, the ball stops for a moment, and then returns back down.
so, final velocity, $v= 0$
suppose it takes time t to reach maximum height.

$v=u+gt$

$
0=65-9.81t$

$t= \frac{65}{9.81}=6.6$

it takes 6.6 s to reach max height.

Maximum height reached, h is given by

$h=ut + \frac{1}{2}gt^2$

$h=(65)(6.6) + \frac{1}{2}(-9.81)(6.6)^2$

$h=215.34\;\; ft$

total height from ground = 4 + 215.34 = 219.34 ft

3. ## thanks so much

Thank you so much for your help!!