Bonnie and Clyde speed down the highway at 120 km/hr, passing a concealed police

Question

Bonnie and Clyde speed down the highway at 120 km/hr, passing a concealed police car that is at rest 1.5 km from the state line. The instant Bonnie and Clyde pass the patrol car, the cop pulls onto the highway and accelerates at a constant rate of 2.2 m/s2. (a) Does the police car catch up with Bonnie and Clyde before they reach the state line? (b) if so, how far is it to the state line from where the cop catches them? If not, how far ahead of the cop are Bonnie and Clyde when the cop reaches the state line?

Explanation / Answer

for bonnie and clyde :

v = speed = 120 km/hr = 33.33 m/s

d = distance for state line = 1.5 km = 1500 m

t = time taken to reach stateline

using the equation

t = d/v = 1500/33.33 = 45 sec

for the police :

Vo = initial velocity = 0

a = acceleration = 2.2

t = time of travel

x = displacement = 1500 m

using the equation

x = Vo t + (0.5) a t2

1500 = 0 t + (0.5) (2.2) t2

t = 36.93 sec

clearly time taken by the police is smaller hence police catch them before stateline

b)

displacement by the police = distance travelled by bonnie

Vo t + (0.5) a t2 = v t

0 t + (0.5) (2.2) t2 = 33.33 t

t = 30.3 sec

D = distance from state line = 1500 - 33.33 x 30.3 = 490.1 m

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