What is the maximum height the rocket reaches?

Question

A rocket takes off from a height of 30 feet with an initial velocity of 150 ft/sec. The equation that models the path that the rocket takes is: (G)x = -16t^2 + 150t + 30. What is the maximum height the rocket reaches?

Answer 1

the function G(t) = -16t² + 150t + 30 tells you the height of the rocket given a time t (in seconds). So we need max height but beforehand we need to find the time the rocket reaches that max height

to find the maximum height requires calculus by the following:

1) find the derivative of G(t) or G'(t)

2) set G'(t) = 0 and solve for t. This the time the rocket reaches the maximum height (NOT the max height itself)

3) plug that t into the original equation G(t) to get the maximum height

I recommend using some kind of graphing calculator to check your answer

Answer 2

Maximum height occurs at t = -b / 2a, or t = -150 / (2)(-16)

Substitute that value and answer.

Answer 3

Velocity v(t) = x'(t) = - 32t + 150 = 0-; t = 150/32 = 4.6875 s

max x(t) = x(4.6875) = - 16·(4.6875)² + 150·4.6875 + 30 = 381.5625 ft