 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/a/solution

Put the station at

(0, 0)

and take B's initial position to be

(0, a)

. Interception after time

t

requires A to cover displacement

(v t, a)

u

u^{2} t^{2} = v^{2} t^{2} + a^{2}, t_{out} = \frac{a}{u ^{2} - v ^{2}} = \frac{5 a}{7 c} = 1.890 days .

The required launch components are

u_{x} = v = 3 c /5

and

u_{y} = u^{2} - v^{2} = 7 c /5

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