Question

A boat A moving with speed 8kmh leaves point p whose position vector is r1=4i+3j heading directly towards point Q whose position vector is r2=2i+5j. At the same time another boat B leaves point 0i+0j. if the velocity of boat B is vector Vba=root2(-5i+3j), find
a. the veloctiy of boat B
b. the timetaken when the boats are close
c. the shortest distance apart

Answer 1

a) |√2(-5i+3j)| = √2 √(5^2+3^2) = √2 √34 = √78
b) The distance at time t is the length of B-A
B = (-5√2 t, 3√2 t)
A = (4-2√2t, 2+2√2t)
B-A = (4-3√2t, 2+5√2t)
|B-A| = 2√(17t^2 - √2 t + 5)
Now find when that is minimum.