Answer to Question #103049 in Mechanics | Relativity for Nimra

Question #103049
A car is travelling at a constant speed of 950m/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 100m/s².how long does it take her to take the car?
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Expert's answer
2020-02-20T09:41:30-0500

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


d=at22.d=\frac{at^2}{2}.

The distance traveled by a car


d=v(t+1).d=v(t+1).

Hence


at22=v(t+1),\frac{at^2}{2}=v(t+1),100t22=950(t+1),\frac{100t^2}{2}=950(t+1),t219t19=0,t^2-19t-19=0,t=20s.t=20\:\rm s.

Finally, the distance traveled by trooper


d=at22=100×2022=20000m.d=\frac{at^2}{2}=\frac{100\times 20^2}{2}=20 \:000\:\rm m.


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