A rocket is fired straight up from a 60 ft. platform with an initial velocity of 96 ft/sec. The height of the rocket, h(t), is found using the function h(t)= - 16t^2+ 96t + 60 where t is the time in seconds.
Find the number of seconds required to reach the maximum height.

Question

A rocket is fired straight up from a 60 ft. platform with an initial velocity of 96 ft/sec.  The height of the rocket, h(t), is found using the function h(t)= - 16t^2+ 96t + 60 where t is the time in seconds.
Find the number of seconds required to reach the maximum height.

ybarrap · Answer

The easiest way is to take the derivative of h(t), which give velocity as a function of time. Then at the very top of the height, the rocket is not moving because it is about to come back down. At that point, velocity is zero. So, set the derivative of h(t) equal to zero and solve for t. This determines when the rocket reaches it's maximum. You should also check that v(0) = h'(0) = 96 ft/sec, which is the rocket's initial velocity. Note that h(0) = 60, the rocket's initial height.

ybarrap · Answer

if you don't know derivatives, plot the function h(t) and find out the t where h(t) begins to get smaller. That's your peak and also the value of t at that point is the number of seconds to get to that point. This will be an estimate.