Question

Lieutenant Wharf, of mass 95.6 kg, is outside the space shuttlecraft Enigma trying to repair a broken warp engine nacelle. He finds he has drifted away from the shuttle while carelessly daydreaming. Miraculously, a stray photon torpedo casing (mass 2,640 kg) appears. Wharf uses this casing to get back to the shuttle by pushing against the casing. If the casing moves directly away from the shuttle after this push with a speed 0.2 m/s, and it then takes him 5.1 seconds to reach the shuttle again, how far away was he from the shuttle, in m?

Answer 1

Since there is no external force applied on the system of Lieutenant and torpedo, So Using momentum conservation:

Pi = Pf

Pi = 0, since initially both Lieutenant and torpedo are at rest

So, Pf = 0

m1*v1 + m2*v2 = 0

m1 = mass of Lieutenant = 95.6 kg

v1 = final speed of Lieutenant = ? (Assuming Lieutenant moves in +ve direction)

m2 = mass of torpedo = 2640 kg

v2 = final speed of torpedo = -0.2 m/s (-ve since it is moving in opposite direction of Lieutenant)

So,

v1 = -m2*v2/m1

v1 = -2640*(-0.2)/95.6

v1 = 5.523 m/s = final speed of Lieutenant Wharf

Now we know that:

distance = speed*time

So time taken by him to reach shuttle = 5.1 sec,

which means

distance traveled by him = d1 = v1*t

d1 = 5.523*5.1

d1 = 28.2 m = original distance of Lieutenant Wharf from shuttle

Let me know if you've any query.