A90-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?

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

here we know that ball will drop down by total distance 3.2 m

so here we know that

now using kinematics

now in the same time it will cover horizontal distance of 0.75 m

so speed of the ball will be

battery with hi vtge high val resist in series