Question

Problem 10:   Suppose a spaceship heading directly away from the Earth at 0.55c can shoot a canister at 0.25c relative to the ship. Take the direction of motion towards Earth as positive. Randomized Variablesv1 = 0.55 c v2 = 0.25 c

  50% Part (a) If the canister is shot directly at Earth, what is the ratio of its velocity, as measured on Earth, to the speed of light?

μ/c =

50% Part (b) What about if it is shot directly away from the Earth (again, relative to c)?

Answer 1

(a)

velocity of ship relative to earth, v_s,e = - 0.55c (away from earth)

velocity of cannister relative to ship, v_c,s = 0.25c

so,

velocity of cannister relative to earth is

v_c,e = -0.55 c + 0.25 c / (1 - (0.55 c * 0.25 c / c²))

v_c,e = - 0.3 c / 0.8625

v_c,e = - 0.3478 c ( away from earth)

so,

ratio = - 0.3478 ( please remove the negative sign, if you need absolute value)

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(b)

now, cannister is shot away from earth, so

v_c,e = -0.55 c - 0.25 c / (1 + (0.55 c * 0.25 c / c²))

v_c,e = -0.8 c / 1.1375

v_c,e = -0.7032 c

so,

ratio = 0.7032 ( please remove the negative sign, if you need absolute value)