Question

In a catastrophic emergency on the space station, the crew will have to leave on escape pods. The pods have limited fuel and are intended to get everyone beyond a safe distance if the station explodes. You need to verify the calculations before signing off on the design. You estimate that debris from an explosion will travel at about 1.8 km s. The pods are designed to launch at a speed of 50 111/s. and will fire their thrusters once they are half a kilometer away from the station (any closer and they risk damaging other pods). The thrusters push the pods faster, giving an acceleration of 4g as they fly away. Assuming an explosion occurs just as the pods reach the thruster-firing point, they need to reach the safe distance of 10 km before the debris catches them. Will you sign off on the design? Your answer must be organized, clear, and complete. See the mastery problem rubric for a reminder of what should be included for a perfect score.

Answer 1

speed of debris = 1.8 km/s

safe distance = 10 km

time taken to reach safe distance = 10 / 1.8 = 5.6 sec

consider the motion of pod :

launch speed , V_o = 50 m/s

distance of thrust firing point = 0.5 km

distance to be travelled to reach the safe point, d = 10 - 0.5 = 9.5 km = 9500 m

a = acceleration = 4 x 9.8 = 39.2 m/s²

using the equation :

d = V_o t + (0.5) a t²

9500 = 50 t + (0.5) (39.2) t²

t = 20.8 sec

so debris will hit the pods