1) Consider the Earth and Moon that are not moving for an instant. The Earth has

Question

1) Consider the Earth and Moon that are not moving for an instant. The Earth has a mass ME and radius RE. The Moon has a mass MM and radius RM. The distance between the Earth and Moon is REM . Find the point on the line connecting the Earth and the moon where there is zero gravitational force on a body of mass m. If you wanted to launch a rocket of mass m from the Earth to the moon, what is the minimum velocity that you would want to fire the rocket?

2)A particle of mass m is bounced elastically up an incline that makes an angle = 26.57 with respect to the horizontal. The particle has an initial speed v0 and initial angle 0 with respect to the incline. Find the value f that the particle makes with respect to the incline when it impacts the incline. Find the initial angle that the particle will rebound by reversing course. For that initial angle find the distance up the incline.

Explanation / Answer

1)

Let the point be distance "x" from the center of earth

For the Force to be 0 at the point

Gravitational field by earth = Gravitational field by moon

GMe / x2 = G Mm / (Rem - x)2

(Rem - x) /x = sqrt (Mm/Me)

Rem / x = 1 + sqrt (Mm/Me)

x = Rem / (1 + sqrt (Mm/Me) )

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