The position vectors, r km, and the velocity vectors, v km/h, of two boats at a certain time are given by ...

Question

Boat A:at 10:00 am rA=6i+10j vA=8i–2j
Boat B:at 10:30 am rB=8i+5j vB=4i+j

... determine the time at which boat B should head out so that the two boats do collide.

Answer 1

If A starts at time 0, and B starts at time k,

(6+8t)i + (10-2t)j = (8+4(t-k-1/2))i + (5+(t-k-1/2))j

so,

6+8t = 8+4(t-k-1/2)
10-2t = 5+t-k-1/2

(k,t) = (-11/8,11/8)

B had to leave at 10:00 - 1:122:30 = 8:37:30

At t=11/8 = 11:22:30, both boats are at (17,7.25)