A car traveling at a constant speed of 21.0 m/s passes a trooper hidden behind a billboard. One second after the speeding car passes the billboard, the trooper sets off in chase with a constant acceleration of 2.60 m/s^{2}.
How long does it take the trooper to overtake the speeding car? Solve this problem by a graphical method. ________ seconds
Initial speed of the car u = 21 m/s
Let t = 0 s when the car passes the trooper.
The trooper starts from rest 1 s after the car passes the billboard. In this 1 s the car would have covered a distance
of 21 m.
Let t' be the time at which the trooper overtakes the car.
Distance covered by car at time t' is
S = 21 + ut' = 21 + 21*t' --------(1)
(The distance is measured from the billboard)
The same distance is covered by the trooper also.
S = 0 + 1/2 * 2.60 * t'^2 ---------(2) (Initial speed of trooper = 0).
Equating (1) and (2)
21 + 21*t' = 2.60*t'^2/2
1.30*t'^2 - 21*t' - 21 = 0
t' = (21 ± (441 + 4*1.3*21)^1/2 )/(2*1.3)
t' = (21 + 23.45)/(2*1.3)
t' = 17.09 second
It takes 17 s for the trooper to overtake the car.
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