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## Homework Statement

A space person is motionless a distance of 500m away from the safety of the spacecraft. The person has exactly 11.32min of air left and the person's mass is 103.2kg, including equipment. The person throws a phaser at a velocity of 50.2km/h away from the space craft in order to get back. I f the mass of the phaser is 5.3 kg, how many minutes of extra air does the person have when they get back to the spacecraft？(Ans: 0.28min)

I attempted to solve it , but get the answer of 0.25min.

please help！

T

## Homework Equations

Conservation and momentum.

P=mv

Ft=mv

Impulse momentum theory

## The Attempt at a Solution

① m1v1+m2v2=m1v1'+m2v2'

v1'=42.97m/min

②t=500/(836.9m/min+42.97m/min) ＝0.57min

③d=v1't=42.97m/min *0.57min=24.42m

④d(remaining)=500m-24m=475.6m

⑤t=d/v=475.6m/ (42.97m/min)=11.07min

⑥t(remaining)=11.32-11.07=0.25min

I try to solve the question, but got the wrong answer. Could anyone help me out？ Thank you so much.