A car traveling at a constant speed of 27.8 m/s passes a trooper hidden behind a

Question

A car traveling at a constant speed of 27.8 m/s passes a trooper hidden behind a billboard, as in the figure. One second after the speeding car passes the billboard, the trooper sets off in chase with a constant acceleration of 3.83 m/s2.

(a) How long does it take the trooper to overtake the speeding car? I put 14.5

(b) How fast is the trooper going at that time? I put 55.6

Can someone show where I am going-- tried 3 times now.

Responses Incorrect: Your answers are incorrect. Your responses are within 10% of the correct values.

Explanation / Answer

Distance travelled by the trooper in time t = 27.8m + distance travelled by the car in time t

=> 0.5* a* (t^2) = 27.8 + 27.8*t

=> 1.925 * (t^2) - 27.8*t - 27.8 = 0

On solving the quadratic eq., we get:
t1 = 15.3805 and t2 = -0.9389 (ignore the negative time)

Hence it will take 15.3805 seconds

Velocity of trooper = 0.5 * 3.83 * (15.3805^2)

= 453.012 m/s

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