NASA has a job interview for a research position. At the interview an applicant
ID: 1529805 • Letter: N
Question
NASA has a job interview for a research position. At the interview an applicant is given the following problem: NASA is testing a new type of rocket fuel. A rocket filled with the new fuel is blasted straight up into the sky with an initial velocity 160 [ft/sec]. At t seconds the rocket is 160t - 16t2 [ft] high. Here are four most important questions NASA is interested in regarding the quality of the new fuel.
1. How high does the rocket go?
2. What are the velocity and acceleration of the rocket when it is 256 ft above the ground on the way up?
3. What are the velocity and acceleration of the rocket when it is 256 ft above the ground on the way down?
4. When does the rocket hit the ground again?
Explanation / Answer
(1)
Position, x = 160*t - 16t^2
v = 160 - 32*t
a = - 32 ft/s^2
At highest position, v = 0
So,
t = 160/32 = 5 s
Max Height , = 160* 5 - 16 * 5^2
Max Height , = 400 ft
(2)
160*t - 16t^2 = 256
Solving for t
t = 2 , 8
At t = 2, Rocket is going up,
v = 160 - 32*2
v = 96 ft/s
a = - 32 ft/s^2
(3)
At t = 8, Rocket is going down,
v = 160 - 32*8
v = - 96 ft/s
a = - 32 ft/s^2
(4)
160t - 16t2 = 0
t = 10 s
The rocket will hit gound again after 10s of launch !!
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