In your new job, you are the technical advisor for the writers of a gangster movie about Bonnie and Clyde. In one scene Bonnie and Clyde are being pursued by a police car. They are 750m from a level railroad crossing travelling at 100 km/hr. A train is 500 meters from the crossing travelling at 130 km/hr. The level crossing is on the state line, and so if they can beat the train, they could evade capture, at least for a while until they become Federal fugitives. They accelerate at a constant rate of 4 m/s2 toward the crossing. The writers want to know if Bonnie and Clyde make it across the crossing before the train.

Explanation:

Velocity of train 130 km /hr

distance of crossing s = 500 m = .5 km

Time taken by train to reach crossing = .5 / 130 = .003846 hr = 13.85 s

Time taken by gangster to reach the crossing = t

initial velocity u = 100km/h = 27.77 m /s

distance of crossing s = 750 m

acceleration a = 4 m /s

s = ut + .5 a t²

750 = 27.77 t + .5 x 4 x t²

2 t² + 27.77 t - 750 = 0

t = - 27.77 ± √(27.77² + 4 x 2 x 750) / 2 x 2

= - 27.77 ±√ ( 771.17 + 6000) / 4

= - 27.77 ±82.28 / 4

= 13.62 s

So this time is less than time taken by train so it will be able to cross the crossing before train arrives .

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