Question

An 80-kg astronaut becomes separated from his spaceship. He is 15.0 m away from it and at rest relative to it. In an effort to get back, he throws a 500 gram object with a speed of 8.0 m/s in a direction away from the ship. How long does it take him to get back to the ship?

Answer 1

The astronaut will take 300 seconds

Explanation:

We can solve this problem by using the law of conservation of momentum.

In fact, the total momentum of the astronaut+object system must be conserved.

Initially, they are both at rest, so their total momentum is zero:

$p=0$

After the astronaut throws the object, their total momentum is:

$p=MV+mv$

where:

M = 80 kg is the mass of the astronaut

V is the final velocity of the astronaut

m = 500 g = 0.5 kg is the mass of the object

v = 8.0 m/s is the velocity of the object

Since momentum is conserved, we can write

$0=MV+mv$

And solving for V,

$V=-\frac{mv}{M}=-\frac{(0.5)(8.0)}{80}=-0.05 m/s$

Which means that he starts moving at 0.05 m/s in the direction opposite to the object.

Now the astronaut needs to cover a distance of

d = 15.0 m

And his speed is

v = 0.05 m/s

Therefore, the time taken is

$t=\frac{d}{v}=\frac{15.0}{0.05}=300 s$

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