Question

A 61kg astronaut (including spacesuit and equipment), is floating at rest a distance of 10 m from the spaceship when she runs out of oxygen and fuel to power her back to the spaceship. She removes her oxygen tank (3.0 kg) and flings it away from the ship at a speed of 15 m/s relative to the ship.

PART A: At what speed relative to the ship does she recoil toward the spaceship?

My attempt: m₁V₁=m₂V₂

(3kg)(15m/s) = (61kg)(V₂)

45 kg*m/s = (61kg)(V₂)

V₂ = .7377 m/s

***The program is telling me that it is wrong but that I am almost there. It says, "Not quite. Check

through your calculations; you may have made a rounding error or used the wrong number of

significant figures.***

***ALSO, I have tried -.7377 m/s and that was completely wrong***

PART B: How long must she hold her breath before reaching the ship?

Answer 1

A)distance at which the astronaut of total mass m=61 kg is at rest is d=10 m.

velocity of the removed mass (m=3.0 kg) v=15 m/s

we have to find out the velocity (V)of the remaining mass (M=61-3=58 kg).So applying law of conservation of energy,

$M*V=m*v$

$V=\frac{m*v}{M}$

$V=\frac{3*15}{58}$

so V=0.7758 m/s

B)Time upto that she must hold her breath is equal to the time taken by the astronaut to reach the spaceship with velocity V=0.7758 m/s travelling a distance d=10.0 m.

so $t=\frac{d}{V}$

t=12.89 sec