Question

A space probe has two engines. Each generates the same amount of force when fired, and the directions of these forces can be independently adjusted. When the engines are fired simultaneously and each applies its force in the same direction, the probe, starting from rest, takes 17.0 s to travel a certain distance. How long does it take to travel the same distance, again starting from rest, if the engines are fired simultaneously and the forces that they apply to the probe are perpendicular?

Answer 1

If in the same direction, thurust is T, and if at ninety degrees, thrust is .707T.

distance=at,
distance=Force/mass* t
time=distance*mass/Force

Case 1: Force=1 unit, time is 17 seconds

distance*mass=time*force=17*1
Case 2: force=.707, time is ?
distance*mass=time*.707
because distance*mass is the same, set the two equations equal, or

time=17/.707=17 sqrt2