# What is the maximum height of the rocket?

demenius

## Homework Statement

A rocket has a body which consists of 0.49kg of material. This body holds 1.47kg of fuel. The fuel is consumed at a rate of 0.49kg/s, and the exhaust speed of the fuel is 60m/s. Assuming that the rocket starts from rest, what is the maximum height the rocket reaches?

## Homework Equations

Note: ∫ln(x)dx = xln(x) - x

## The Attempt at a Solution

None. Don't know where to start.

## Answers and Replies

Mentor
Start by determining the thrust (force) that the engine produces as it burns fuel at the given rate with the given exhaust speed. Then find an expression for the mass of the rocket+propellant with respect to time. With these you can write an expression for the acceleration of the rocket w.r.t. time (remember to include gravitational acceleration). With the acceleration function you can find velocity and distance with some calculus.

The rocket will have some height and speed when the fuel runs out, so it becomes a simple projectile after that.