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 40.2 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

Let the mass of probe be m and Force applied by each engine be F

in the first case, force acting on probe=2*F=2F

acceleration=a₁=2F/m

time taken =40.2 seconds

In the second case, forces are perpendicular to each other.Force on proble=1.414*F

acceleration=a₂=1.414F/m

a₁/a₂=2/1.414=1.414

We know, distance travelled = s=ut+0.5at²

u=0 since the probe strats from rest

s=0.5*a₁*t₁²

s=0.5*a₂*t₂²

a₁*t₁²=a₂*t₂²

t₂/t₁=sqrt(a₁/a₂)=sqrt(1.414)=1.189

t₂=1.189*t₁=1.189*40.2=47.8 seconds

Required answer is 47.8 seconds