Apply Newton's second law to each case, slowing down or speeding up, and use this to find the spacecraft's wei

Question

A spacecraft descends vertically near the surface of Planet X. An upward thrust of 25.0 kN from its engines slows it down at a rate of 1.20m/s^2, but if an upward thrust of only 10.0 kN is applied, it speeds up at a rate of 0.80m/s^2.

Answer 1

net force = thrust - gravity

gravity = mass x acceleration of gravity on planet X

acceleration = (net force)/mass

So you have two equations, one for thrust = 25.0 kN and one for 10.0kN, in two unknowns, mass and acceleration due to gravity.

(Don't forget that one acceleration is positive at 1.2 m/s^2 while the other is negative at -0.8 m/s^2.)