Explanation Write the expression from the conservation of energy. K + U = K 0 + U 0 (I) Here, K is the final kinetic energy, U is the final gravitational potential energy of the rocket, K 0 is the initial kinetic energy, and U 0 is the initial gravitational potential energy of the rocket. The gravitational potential energy of the rocket is, U = − G M E m h + R E (II) Here, G is the gravitational constant, R E is the radius of the Earth, M E is the mass of the Earth, m is the mass of the rocket, and h is the distance from Earth’s center at the peak. The kinetic energy of the rocket is, K 0 = 1 2 m v 0 2 (III) Here, v 0 is the speed of the rocket. The initial gravitational potential energy of the rocket is, U 0 = − G M E m R E (IV) Here, R E is the radius of the Earth. Conclusion: Substitute the equations (II), (III), and (IV) in equation (I). 0 − G M E m R E + h = 1 2 m v 0 2 − G M E m R E − G M E R E + h = 1 2 v 0 2 − G M E R E G M E R E − G M E R E + h = 1 2 v 0 2 Solve the above relation for v 0 . G M E ( 1 R E − 1 R E + h ) = 1 2 v 0 2 v 0 2 = 2 G M E ( 1 R E − 1 R E + h ) v 0 = 2 G M E ( 1 R E − 1 R E + h ) Substitute 6

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Centripetal Force

A particle, body, object or certain mass while travelling in a rotational path or semicircular path, experiences an inertia force. If that inertia force pulls the towards the inward of the imaginary circle in the rotation, it is termed as centripetal for…

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Chapter 8, Problem 35E

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