Question

A couple of astronauts agree to rendezvous in space after hours. Their plan is to let gravity bring them together. She has a mass of 60.0 kg and he a mass of 76.0 kg , and they start from rest 25.0 m apart. Find his initial acceleration.

Answer 1

Explanation: This is can be solve by knowing Newton's law of universal gravitation. Two masses will be attracted to each other by a force that will be proportional to their masses. The following equation describes it.

`F = G (M1 * M2)/(d^(2) )`

Knowing both their masses, the distance and the G, which is the universal gravitation constant (6.674×10−11)
`N * (m/kg)^(2)`, give us the following results:

F =
`4.869 * 10^(-10)`

With the force, we can calculate the acelaration for each body using Newton's Law

F = m*a

Accomodating the equation

F / m = a

For the male austronaut which weight 76 kg

a =
`64.065 * 10^(-13)  (m/s)`