Question

A rocket is shot straight into the air at an initial velocity of 120 feet/second. The height of the rocket after t seconds is given by the equation h = 120t – 4t2. After how many seconds will the rocket reach its maximum height?

Answer 1

Vertex of a parabola: -b/2a

Answer 2

first you must rearrange your equation in receding powers

Answer 3

A.900 seconds
B.120 seconds
C.30 seconds
D.15 seconds

Answer 4

This can be solved using calculus.

Given h = 120 t - 4 t^2

Differentiate,
dh/dt = 120 - 8t

Differentiate a 2nd time, d2h/dt2 = -8
This shows that whatever stationary point it is a maximum turning point, which is what you want.

Returning to dh/dt
equate dh/dt= 0 to find the value of t which makes h maximum.
120-8t = 0
8t=120
t=15

When t = 15, h is maximum

Answer 5

Thanks, so D?

Answer 6

@tiaph , first of all you gave the answer without any talk about how to go about the problem. This caused you to do it in a calculus fashion when there is two ways to solve it. No where did you help smarty come to this answer as you never asked what class he was taking.

Answer 7

Because i saw you typing "vertex of the parabola... " so i assume you are gonna offer the geometrical or graphing method to solve the question. I am just using calculus to provide a 2nd method of answering. I assure you when i answer question i do my best to make my explanation as clear and succinct as possible, so people understand what i am doing. I apologize, if my seemingly rash and unconcerned answer provide much distress to you.