Answer to Question #103048 in Mechanics | Relativity for Nimra

Question #103048
A car is travelling at a constant speed of 780m/s. Passes a trooper hidden behind a Billboard one second of the car passes the Billboard, the trooper sets out from the Billboard to catch it, acelerating at a constant speed of 90m/s².how long does it take her to take the car?
1
Expert's answer
2020-02-20T09:41:16-0500

Let the time of motion of the trooper is t, then distance traveled by her


"d=\\frac{at^2}{2}."

The distance traveled by a car


"d=v(t+1)."

Hence


"\\frac{at^2}{2}=v(t+1),""\\frac{90t^2}{2}=780(t+1),""t^2-17.3t-17.3=0,""t=18\\:\\rm s."

Finally, the distance traveled by trooper


"d=\\frac{at^2}{2}=\\frac{90\\times 18^2}{2}=14\\:580\\:\\rm m."


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