Help!‚ÄčA car traveling at a constant speed

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A car traveling at a constant speed of 36.4 m/s passes a trooper hidden behind a billboard. One second after the speeding car passes the billboard, the trooper sets in a chase after the car with a constant acceleration of 3.96m/s^2.

how long after the trooper starts the chase does he overtake the speeding car?

Oct 4th, 2015

Thank you for the opportunity to help you with your question!

Thank you for the opportunity to help you with your question!

the car's speed is 36.4 * 5/18 = 10.11 m/s

the troop chases with an initial velocity u = 0

and acceleration = 3.96m/s^2

After a time t sec

the distance covered by the car  = 10. 11 * (t+1)

and by the trooper = 0.5* a*t^2

on equating the distance from both the equations wee get a quadratic equation:

0.5* a*t^2 - 10. 11 * t  - 10. 11= 0

on solving for t , we get t = 11.92 sec

so the chase will be complete at (11.92+ 1) = 12.92 sec

Please let me know if you need any clarification for the doubts. I'm always happy to answer your questions. Looking forward to help you again. thank you. :)
Oct 4th, 2015

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