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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.

Answer 1

Put t=0 in Robin's moving equation. That gives you (-3,5) which is the point from which Robin starts to move. Now consider that for every hour Robin is moving 6 Km up and 8 Km to the right. Using Pythagoras theorem, he moves 10 Km every hour. After two hours, he's 20 Km away from the origin. AT this point Casey reaches the same origin from which Robin started. So, Casey is always 2 hour behind Robin. Thus, Casey's moving equation will be:

rule(x,y) = (-3+8*(t-2),5+6*(t-2))

which is:

rule(x,y) = (-19+8*t,-7+6*t)