A 70-kg astronaut (including spacesuit and equipment) is floating at rest a distance of 13 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. Required:
a. At what speed relative to the ship does she recoil toward the spaceship?
b. How long must she hold her breath before reaching the ship?

Explanation:

mass of the astronaut including the spacesuit,

distance of astronaut from the spaceship, d = 13 m

mass of the oxygen tank, m = 3 kg

Speed of tank with respect to spaceship,

a)

Using the conservation of linear momentum:

total momentum before collision = total momentum after collision

b)

She mush hold her breath until she reaches the spaceship, i.e.

you'd use the equation that establishes a relationship between  energy  and  wavelength, which looks like this

e=h⋅cλ, where

λ  - the wavelength of the photon; c  - the speed of light, usually given as  3⋅108m/s; h  -  planck's constant, equal to  6.626⋅10−34j s

plug the value you were given for the energy of the photon in the above equation to get the wavelength

e=h⋅cλ⇒λ=h⋅ce

λ=6.626⋅10−34js⋅3⋅108ms−1.257⋅10−24j=1.581⋅10−1m