Question

A 90-kg astronaut is stranded in space at a point 6.0 m from his spaceship, and he needs to get back in 4.0 min to control the spaceship. to get back, he throws a 0.50-kg piece of equipment so that it moves at a speed of 4.0 m/s directly away from the spaceship. (a) does he get back in time? (b) how fast must he throw the piece of equipment so he gets back in time?

Answer 1

Momentum = 0.5 * 4 = 2
to conclude the man’s velocity after he throws the piece of equipment, divide this number by the man’s mass.

v = 2/90

This is about 0.0222 m/s. To know if he can move 6 meters at velocity in 4minutes, use the following equation.

d = v * t, t = 4 * 60 = 240 s
d = 2/90 * 240 = 5⅓ meters.

This is ⅔ of a meter from the spaceship. To know the velocity that he must have to move 6 meter, use the same equation.

6 = v * 240
v = 6/240
This is about 0.00416 m/s.
His final momentum = 90 * 6/240 = 2.25

To know the velocity of the package, divide this number by the mass of the package.
v = 2.25/0.5 = 4.5 m/s