Calculus , algebra

Question

A rocket is launched upward with a initial velocity of 86ft/sec . It’s height after T seconds is given by 86t-16t2 . How high will the rocket go ?

Answer 1

From kinematics,

v(t) = v₀ + at = v₀ - gt = 86 - 32t

It keeps climbing until v(t) is zero, so set

86 - 32t = 0

and solve for t. Then plug the result for t into the equation for h(t) and get maximum height.