# Rocket Kinematics Problem

## Homework Statement

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?

## Homework Equations

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

## The Attempt at a Solution

I'm lost...

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

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

lewando
Homework Helper
Gold Member
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:
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?

lewando
Homework Helper
Gold Member
Yes, actually!

Thank you very much for your help! :)