A rocket is shot vertically off the ground with an initial velocity of Vo ft/sec. The equation that gives its height s above the ground at time t is: s= s(t) = -16t^2 + Vot What does one do to find time when the rocket reaches its highest point?

1 Answer
Mar 25, 2018

#=>t = v_0/32# seconds

Explanation:

You have an equation that gives position. You can take the derivative to find an equation that describes the velocity. Then find the time at which the velocity is #0#, as this will be the moment the rocket is at its maximum height.

#s(t) = -16t^2+v_0t#

#v(t) = s'(t) = -32t+v_0#

#v(t) = -32t+v_0 = 0#

#=>-32t = -v_0#

#=>t = v_0/32#

So #t = v_0/32# seconds is when the rocket will be at its max height.