Practice Problem 2-98 (p 2-45)

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:

x_c = v_0ct

Position of the police cruiser:

x_p = v_0pt + ½ at² with x_0p = 0

Correct!

In fact, all three methods will give the correct (and same) answer.

Method a

x_c = v_0ct = 290 = 18t

t = 16 s.

Method b

x_p = v_0pt + ½ at² = 290 = 0 + ½ (2.2)(t²)

t² = 2(290)/(2.2) = 264

t = 16 s.

Method c

x_p = x_c

v_0ct = ½ at²

t = 2(v_0c)/a = 2(18)/(2.2) = 16 s.

Methods (a) - (c) all provide the same answer to part (b) of the original question listed above.

This concludes the Socratic Car Chase question.