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Calculate the vertical distance through which the moon falls in 2 days
Asked by Amit | 21 Mar, 2019, 09:48: AM
answered-by-expert Expert Answer

The earth and the moon are attracted towards each other by the force of attraction. The path of the moon fall is like a projectile which has both horizontal and vertical distance.

The moon fall can occur only at one position when it is above the earth. It revolves around the earth. If there was no earth, then the path of the moon from the highest point would be a straight line path; but the earth bends its path to form a circular orbit.

We know that the radius of moon s orbit is 3.8 * 108 m

Period of moon s revolution = 27.3 days = 2.4 * 106 seconds

The velocity = ωR = 2 * 22/7 * R / T = 2 * 22/7 * 3.8 * 108 / 2.4 * 106 = 103m/s

The acceleration is centripetal acceleration = v2/R = (103)2 / 3.8 * 108 m/s2 = 2.7 * 10-3 m/s2

At a given time, the horizontal distance covered is given by vt and the vertical distance covered is ½ at2

X= vt = 103 * 2 * 24 *60 *60 = 1728 * 105 m  (9 digit number in m)

Y = ½ at2 = ½ * 2.7 * 10-3 * (2 * 24 * 60 *60)2 =   4,03,107.84 m (6 digit number)

Thus, the horizontal distance covered is more than the vertical distance covered.

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