Car Chase

A car (c) with one headlight burned out is traveling at a constant speed of 18 m/s and passes a stopped police car (p). The car is pursued immediately by the police cruiser, which has a constant acceleration of magnitude 2.2 m/s2.
(a) How far does the police cruiser travel before catching the other car?
(b) At what time will this occur? (Hint: Graphing may help to visualize this problem.)

Accumulated solution:

Position of the car:

xc = v0ct

Position of the police cruiser:

xp = v0pt + ½ at2 with x0p = 0

Correct!

Set xp = xc = x and eliminate t.

Let's do it!


From the first equation: t = x/vc.

Substitute this into the second equation:

x = ½ a(x/vc)2

Therefore,

x = 2vc2/a = 1(18)2/(2.2) = 2.9x102 m.

This is the answer to part (a) of the original question listed at the top.

To determine the time elapsed until the cruiser catches up with the car, select "Car Chase 6" from the Navigation tree..