Question

An astronaut in space cannot use a scale or balance to weigh objects because there is no gravity. But she does have devices to measure distance and time accurately. She knows her own mass is 78.4 kg , but she is unsure of the mass of a large gas canister in the airless rocket. When this canister is approaching her at 3.40 m/s , she pushes against it, which slows it down to 1.30 m/s (but does not reverse it) and gives her a speed of 2.50 m/s. What is the mass of this canister?

Answer 1

Answer:

93.33 kg

Explanation:

We are given that

Mass of astronaut=m'=78.4 kg

Initial velocity of canister,u=3.4 m/s

Final velocity of canister,v=1.3 m/s

Initial velocity of astronaut=u'=0

Final velocity of astronaut,v'=2.5 m/s

We have to find the mass of canister.

According to law of conservation of momentum

$mu+m'u'=mv+m'v'$

Using the formula

$m(3.4)+78.4\times 0=m(1.3)+78.4(2.5)$

$3.4m=1.3m+196$

$3.4m-1.3 m=196$

$2.1 m=196$

$m=\frac{196}{2.1}=93.33 kg$

Mass of canister=93.33 kg