Question

Superman throws a golf ball horizontally so hard that after a while it hits him in the back! He concludes correctly that the ball must have flown once around the Earth! Calculate how long the ball was in the air. Use that the Moon takes 27.3 days to revolve once around Earth and is 380,000 km away from the Earth, while the radius of the Earth is 6370 km.

Start each problem with a SKETCH carefully labeling all quantities you are going to use. Then write what is GIVEN, what is WANTED, proceed to your APPROACH, and finish with the SOLUTION.

Answer 1

when an object revolves around earth under the influence of gravitational field, the gravitational force of attraction balances the centripetal force. When the moon revolves around earth, we have

...................(1)

where G is Gravitation constant, M is mass of earth , m is mass of moon , v is the tangential speed of revolution and R is radius of circular path of moon so that centre of earth is centre of circular path of moon.

From eqn.(1) , we get ,

.................(2)

If ball thrown by superman is moving in a circular path bery near to earth surface , then we write eqn.(2) for ball thrown by superman as

.....................(3)

where vb is tangential speed of ball and RE is radius of earth. From eqn.(2) and eqn.(3), we get

tangential speed v of moon = ( 2 R ) / T = ( 2 3.8 108 ) / ( 27.3 24 3600 ) = 1012 m/s

Hence vb = 7.724 1012 = 7817 m/s

Hence when superman throws a ball with speed 7817 m/s , the ball revolves around earth and hits him back