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 24.4 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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nuuk nuuk · Answer 1 · 2019-10-10T07:59:46+02:00

Answer:29.01 s

Explanation:

Given

First two engine applies Force in same direction

Considering F be the magnitude of each force then

net Force is 2F

Let the distance travel be s

[tex]s=ut+\frac{at^2}{2}[/tex]

here [tex]a=\frac{2F}{m}[/tex]

where m is the mass of Space Probe

[tex]s=0+\frac{2F(24.4)^2}{2m}[/tex]

[tex]s=\frac{595.36F}{m}[/tex]----1

If the force actin in perpendicular direction

then [tex]F_{net}=\sqrt{F^2+F^2}=\sqrt{2F^2}[/tex]

[tex]F_{net}=\sqrt{2}F[/tex]

[tex]a=\frac{\sqrt{2}F}{m}[/tex]

[tex]s=ut+\frac{at^2}{2}[/tex]

[tex]s=0+\frac{\sqrt{2}Ft^2}{2m}[/tex]------2

From 1 & 2 we get

[tex]\frac{595.36F}{m}=\frac{\sqrt{2}Ft^2}{2m}[/tex]

t=29.01 s