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Q1 An astronaut on the moon, from the moon lander which is 10 m high, can just see the moon disappearing over the horizon. The driver of the rover communicated that he has covered 5895 m away from the lander, in a straight line. Estimate the radius of the moon. Draw a diagram. Explain how you arrive at or derive an equation. Solve the equation rover

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Answer #1

Here, we have been given height h above the surface as 10 m

We have also been given the distance to horizon (d) (straight line) as 5895 m

we need to find the radius of moon

therefore, we can use Pythagoras theorem

d2 = (R+h)2 - R2

d2 = R2 + 2Rh + h2 - R2

d2 = 2Rh + h2

58952 = 20R + 100

R = 1737546.25 m

R = 1737.55 Km

or

R = 1738 Km

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