# Physics

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 44.1 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?

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1. The vector sum of the two engine thrusts, fired at right angles to one another, is sqrt2*T, where T is the thrust of a single engine.

If they fire in the same direction, the total thrust is 2 T.

The acceleration will be 1/sqrt2 = 0.707 as large with the engine thrust axes at right angles.

The time to travel a distance D while accelerating at a rate a is
t = sqrt(2 D/a)

With acceleration reduced by a factor 1/sqrt2, the time to travel D will be increased by a factor 2^(1/4) = 1.189, making it 52.4 seconds.

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