An astronaut in space cannot use a conventional means, such as a scale or balance, to determine the mass of an object. 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 3.50 m/s, she pushes against it, which slows it down to 1.20 m/s (but does not reverse it) and gives her a speed of 2.40 m/s. What is the mass of this canister

81.81 kg

Explanation:

= Mass of person = 78.4 kg

= Mass of canister

= Initial velocity of person = 0

= Initial velocity of canister = 3.5 m/s

= Final velocity of person = 2.4 m/s

= Final velocity of canister = 1.2 m/s

The momentum balance in the system is given by

Mass of the canister is 81.81 kg.

see the picture for the vector

the magnitude of the vector by pythagorean theorem

r = √( (-10)^2 + (3)^2 ) = √109

magnitude = √109 units

the direction angle between vector and x-axis is

tan^(-1)(3/10) = 16.699

so the direction is approximately 16.7 degrees north of west