 Solution

ID: past-exam-of-the-physics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2013/paper-1/section-b/b8/b/solution

Between launch and interception,

Δ x = v t_{out}

. The time-coordinate Lorentz transformation therefore gives

Δ t_{B} = γ_{v} (t_{out} - \frac{v ^{2} t _{out}}{c ^{2}}) = \frac{t _{out}}{γ _{v}}, Δ t_{B} = \frac{4 a}{7 c} = 1.512 days .

This is an elapsed coordinate time in B's inertial frame, not the travel time on A's clock. The latter would be

t_{out} / γ_{u} = 3 a / (7 c)

 New to topics? Read the docs here!