Two cars start moving from the same point. One travels south at 50mph and the other travels west at 35 mph. At what rate is the distance between the cars changing two hours later?

Answer 1

Robert

You need an expression for the coordinates of each car t hours after the start.

Using these find the distance (s) between the cars t hours after the start.

Then find ds/dt when t=2.

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I will do the problem with changed numbers (40, 20, 3).

After t hours, first car will be at (0,-40t) and second car at (-20t, 0)

Using distance formula s² = (0--20t)² + (-40t-0)² = 400t² + 1600t² = 2000 t²

So s = t √ 2000

ds/dt = √ 2000

So after 3 hours distance between them is increasing by √2000 miles per hour.

You could also find the position of each at 2 and 2.1 hours, find the distance between them at 2 and 2,1 hours, take the difference and divide by 0.1, that will give approximately the same answer.

Using my model hopefully you can solve your problem now.

Mike