Rocket Kinematics Problem

1. Jul 2, 2013

caveman127

1. The problem statement, all variables and given/known data
You must determine the acceleration of a rocket so that its equipment can be designed to survive. The rocket will have a burn time of t = 30 seconds, during which time it flies has a constant acceleration a. Call this Phase 1. After the fuel is exhausted the rocket enters free fall. Call this Phase 2. The total flight time is 300s.

a) what should you make the acceleration of the rocket a when the engine is on?
b)what is the maximum altitude of the rocket

//So I don't even know where to start or what part a is asking. What is the condition for the equipment to survive?

2. Relevant equations
x=x0+v0t+(1/2)at^2

3. The attempt at a solution

I'm lost...

2. Jul 2, 2013

lewando

I think none of the equipment survives at the end of the free-fall phase, when t= 300s--so don't worry about that.

3. Jul 2, 2013

caveman127

Yeah that is what I figured as well, but this doesn't really help me solve the question haha.

4. Jul 2, 2013

lewando

So you have two phases where the acceleration is constant, but different. You need to come up with 2 distinct [edit: sets of] equations, each describing the 2 time segments. A third equation might relate the 2 time segments to the total flight time.

Last edited: Jul 2, 2013
5. Jul 2, 2013

caveman127

Hmm okay so....
using x = x0 + v0t + 1/2at^2 for phase one i find that x = 1/2a(30)^2

Phase two I know it hits ground so final x is 0. The inital x for this phase is x from phase 1 so...

-x = V0(270s) - 1/2(g)(270)^2

V0 is the final velocity for phase 1.

V = V0 + at => phase 2 V0 = a30.

Inputing for V0 and -X in phase two I got:
-.5(a)(30^2) = a(30)(270) - (.5)(9.8)(270^2)

Solving for a I got... 41.8 m/s^2 for part a.

Does this look valid?

6. Jul 2, 2013

lewando

Yes, actually!

7. Jul 2, 2013

caveman127

Thank you very much for your help! :)