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
x = xc = xp = 290 m.
To find the time elapsed until they meet we should:
(a) Insert x = 290 m in the first equation and solve for t.
(b) Insert x = 290 m in the second equation and solve for t.
(c) Equate the two (xc and xp)
and solve for t.