An astronaut with a total mass M (including his equipment) has been accidentally separated from his shuttle and is at rest with respect to the ship at a distance d away. His tank contains a mass m, of oxygen (m, M) and is equipped with a nozzle through which the gas can be very rapidly ejected at an average speed of ve. He must release oxygen for propulsion to get back to the spacecraft but also needs oxygen for breathing. He breathes oxygen at a rate of R .

a. If he releases an amount m of oxygen for propulsion, what speed V will he acquire? How long will it take him to reach the spacecraft?

b. How long can he breathe on the remaining oxygen?

c. If he is to return successfully to his craft, his breathing time, tb must be equal to (or greater than) his travel time tr. What condition does this place on m ?

d. Calculate how much oxygen the astronaut may safely release for propulsion if M = 100 kg, m, = 0.5 kg, d = 45 m, Ve = 50 m/s, and R = 2.5 X 10-4 kg/s