Question

A car is travelling at a constant speed of 450m/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 25m/s².how long does it take her to take the car?

Answer 1

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

$$\frac{at^2}{2}=v(t+1),$$ $$\frac{25t^2}{2}=450(t+1),$$

$$t^2-36t-36=0,$$

$$t=6 (3 + \sqrt{10})\:\rm s.$$

Finally, the distance traveled by trooper

$$d=\frac{at^2}{2}=\frac{25\times (6 (3 + \sqrt{10}))^2}{2}=462\:\rm m.$$