A 70-kg astronaut floating in space in a 110-kg MMU (manned maneuvering unit) experiences an acceleration of 0.029 m/s2 when he fires one of the MMU’s thrusters. (a) If the speed of the escaping N2 gas relative to the astronaut is 490 m/s, how much gas is used by the thruster in 5.0 s? (b) What is the thrust of the thruster?

Solution 61E Step 1 of 4: In the given problem, the mass of the astronaut m= 70 kg and in MMU of m =110 kg. 1 He experiences an acceleration of a=0.029 m/s when he fires. Here we need to calculate the amount of (N )ga2 used by the thruster in time dt= 5s where the escaping speed of gas is v ex490 m/s. Given data Total mass, M=m+m =70 kg + 110 kg=180 kg Acceleration, a=0.029 m/s 2 Time interval, dt= 5s External speed, v =ex 490 m/s (negative as it is opposite to the motion of rocket) To find, Amount of gas, dm = The thrust force, F= Step 2 of 4: (a) If the speed of the escaping N2 gas relative to the astronaut is 490 m/s, how much gas is used by the thruster in 5.0 s Using the acceleration equation, vexdm a = M dt Solving for mass, M a dt dm = vex