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?
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))
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.