A 2000 kg space probe is moving rightward in empty space along the x axis at 12 m/s. One of the probe’s rockets is fired providing a thrust of 1800j N along the y axis. The rocket fires for 1.5 s.

Question

How can I derive the equation for the trajectory of the probe during the time the rocket is fired using the formula y = a function of x and compute the final speed of the rocket at the end of the 1.5 s?

Answer 1

Write and solve separate differential equations for the x and y coordinates, during the rocket firing. You will end up with separate equations for x and y.

Once you have those functions, try to write y as a function of x. The Vx velocity component will remain 12 m/s.
That means x = 12 t, if position is measured from the time zero location.

Then derive a separate equation for Vy = dy/dt

The speed is sqrt[Vx^2 + Vy^2] = sqrt[144 + Vy^2]