A space probe has two engines. Each generates the same amount of force when fire

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 38.0 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?

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 38.0 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? Number units the tolerance is +/-2%

Explanation / Answer

net force probe gets = 2F cos45 = Sqrt(2) F

for 2F force it takes 38 secs

Force is proportional to acceleration

let distance travelled = d

d is same

so 0.5(a)(38^2) = 0.5(a/(sqrt2))(t^2)

so t = 45.12 secs

so for second space craft it takes 45.12 secs

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