I don't know how to do this physics problem!!?

Question

A rocket rises vertically, from rest, with an acceleration of 3.2m/s(squared) until it runs out of fuel at an altitude of 1200m. After this point, its acceleration is that of gravity, downward. a) What is the velocity of the rocket when it runs out of fuel? b) How long does it take to reach this point? c) What maximum altitude does the rocket reach? d) How much time (total) does it take to reach maximum altitude? e) With what velocity does the rocket strike the Earth? f) How long (total) is it in the air?

Answer 1

a) 7,680m/s

b) 783.67 secs

c) 3,010,506.122 meters

d) 1,567.347 secs

e) 7,680 m/s

f) 3,134.694 secs

I think these are enough. He he.

Answer 2

First start with the displacement formula :x = ViT + .5at^2

Vi = 0, a=3.2, x=1200

solve for t (this will give you the answer to b)

Second use the final velocity equation Vf^2 = Vi^2 + 2ax to find the final velocity. (this gives you a)

Now use the displacement formula again, but this time starting from the point it run out of fuel. Vi will equal the the answer to a, and acceleration will equal -3.2 (the acceleration of gravity in the opposite direction from its initial motion). the time will be equal to the time going up (it's the same problem in reverse, while powered it is accelerating from 0 - some speed at 3.2, once it runs out it is deceleration from that speed to 0 at 3.2). This will give you how far past 1200 meters it went. Once you have that add it to 1200. As I think of it you could save the time, it will be 1200, so a total height of 2400m. this is c. total time you already have (just add the two times together. Then to get e, you just need to use the displacement formula to solve for t and plug that into the final velocity formula. (remember, because it is falling Vi = 0). Now you have the time going up, and the time coming down, so adding them together gives you f.



thanks for the correction cw, I don't know why I was thinking 3.2 m/s^2 was a due to gravity. *foot in mouth*

Answer 3

Sorry will that's not right...

The two equations you need are:

D= Di + ViT +1/2AT^2    &   V= Vi +AT

So initially 1200 is your height where acceleration ends, Vi is 0 since you start with no velocity, and A is 3.2 (assuming gravity is already accounted for based on the probelm statement)

So solve the first equation for T and T = 27.386s

Now you need your velocity at this point, use the second equation this time and solve for V.  V= 87.6356m/s

Now you need the max altitude, back to equation 2 except now your fuel is out so the acceleration of gravity acts against you (9.81m/s^2) and you have an initial velocity.  Your final velocity is 0 at your maximum altitude.  Solve for T.  T=8.933s so your max time is 27.386s+8.933s

Next equation 1 again using T=8.933 and your initial velocity and time and Di of 1200.  Solve for D.  D= 1591.46m.

Last step, equation 1 again.  your final height is 0, initial is 1591.46 from the previous step, Vi is 0 and A is gravity.  Solve for T, your time to fall.  T= 18.01s.  Your total flight time is all three T's for each portion of the flight.