calculate the vertical distance through which the moon falls in 2 days
Answers
Answer: 403,107 km is the answer. Here is your explanation . If you like my answer then follow me .
Explanation:
The earth and the moon are attracted towards each other by the force of gravitation. The path of the moon fall is like a projectile which has both vertical distance and horizontal 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.
So
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 = 103 m/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 at^2
Y = ½ at2 = ½ * 2.7 * 10-3 * (2 * 24 * 60 *60)2 = 4,03,107.84 m .
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