Question

Robin is moving on the xy-plane according to the rule (x, y) = (-3 + 8t, 5 + 6t), with distance measured in km and time in hours. Casey is following 20 km behind on the same path at the same speed. Write parametric equations describing Casey's position. What if Casey was following 17 km behind?

Answer 1

Let Casey’s position be given by (x,y) = (-3+8r,5+6r). Then the distance between Robin and Casey is ?[{(-3+8t)-(-3+8r)}²+{(5+6t)-(t+6r)}²]= ?[ 64(t-r)²+36(t-r)²] = 10(t-r). Hence 10(t-r) = 20 so that t-r = 2 and r = t-2. Thus, Casey’s position is given by (x,y) =(-3+8t-16,5+6t-12) = (-19+8t, -7+6t).

However, if Casey was following 17 km behind, then 10(t-r) = 17 or, t-r = 1.7 or, r = t-1.7. Then, Casey’s position is given by (x,y) =( -3+8t-13.6, 5+6t-10.2) = (-16.6+8t, -5.2+6t).