# Rocket in space

by tamref
Tags: rocket, space
 P: 5 1. The problem statement, all variables and given/known data A rocket is travelling with a speed 20 km/s in a non-gravity space. To fix the direction of motion, it turns on an engine, which pushes the gasses with constant speed 3 km/s w.r.t. the rocket perpendicularly to the direction of its motion. The engine is on till the mass of the rocket declines for 1/4 of the initial. For what angle has the rocket changed the direction of motion and what is its final speed? 2. Relevant equations x-axis: d( p(rocket) ) = - d( m(gasses) ) v(gasses) cos( alpha+d(alpha) ) dm/dt * v(rocket_final) + dv/dt m( rocket_new )= - dm/dt * v(gasses) (cos(alpha)cos(d(alpha)) - sin(alpha)sin(d(alpha)) ) dm/dt * v(rocket_final) + dv/dt ( m- dm/dt *t) = - dm/dt * v(gasses) *cos(alpha)cos(d(alpha)) 3. The attempt at a solution I tried to express the change in momentum of the rocket w.r.t. the angle of motion like above for both x- and y- axis, but I get unknown velocity and angle.
 PF Patron HW Helper P: 1,955 Taking the direction of motion of the rocket to be the x-axis, write the momentum conservation equation in the y direction. This will give you the final velocity of the rocket in the y direction. Now, you know both the x and y components of the final velocity, and you can calculate the angle that the velocity makes with the x-axis using trigonometry. (Hint: Draw a picture. What is tan(θ) in terms of Vx and Vy?)
 P: 5 Thank you, dx. But the problem I see is, that the direction of gasses also changes with moving rocket. Therefore also Vx changes. The whole momentum does not go into Vy.
PF Patron
HW Helper
P: 1,955

## Rocket in space

The direction of motion changes, but the orientation of the rocket stays the same. So the direction in which the gas is ejected is the same.
 P: 5 What refers orientation of the rocket to, dx? I thought of this problem again and maybe this is a solution. Let us say, that the rocket would push the gasses with a given Vr=3 km/s in front of itself. Then its final Vx would be 19,2 km/s. On the other hand, if the rocket would push the gasses with a given Vr perpendicularly to the initial direction of motion, its final Vy would be 0,86 km/s. Therefore in any case 0

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