Question

Simon launches a T-shirt from a cannon straight up with the initial velocity of 96 feet per second. The height of the T-shirt is represented by h(t) = -16t2 + 96t + 6, where h(t) is the height in feet and t is the time in seconds after Simon launches the T-shirt. How long does it take the T-shirt to reach its maximum height

Answer 1

3 secs

Explanation:

Given the height of the T-shirt represented by the equation

h(t) = -16t² + 96t + 6

velocity v(t) =
`(dh(t))/(dt)`

v(t) = -32t+96

At maximum height, the velocity of the t-shirt is 0ft/s

Substitute v= 0 into the velocity function and calculate the value of t:

0 = -32t+96

Re-arrange

-32t+96 = 0

-32t = -96

t = -96/-32

t = 3secs

Hence it takes 3seconds for the T-shirt to reach its maximum height.