- #1

maca_404

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**Working with two moving targets ??**

Hey guys, Here is the question I am working on

"A car traveling at a constant speed of 80kmh passes as stationary motorcycle policeman. The policeman sets off in pursuit, accelerating to 80kmh in 10 seconds and reaching a constant speed of 100kmh in another 5 seconds. At what time will the policeman catch up with the car. "

I have worked this out so far 80 km h–1 = 22.222 m s–1

and 100 km h–1 = 27.778 m s–1

Let the required time = t.

The distance traveled by the policeman in the first 10.0 s

= 0.5(22.222 m s–1)(10 s) = 111.111 m,

and in the next 5.0 s he travels a distance of 0.5(22.222 m s–1 + 27.778 m s–1)(5.0 s)

= 125 m.

When the policeman catches up with the car, it is

(22.222 m s–1)t = 236.111 m + (27.778 m s–1)(t – 15 s)

and so t = 32.5 s.

So I have the correct answer but to find the answer I just used trial an error till I got the correct time. What I want to know is surely there is an easier way to work out the answer without having to take a stab in the dark. I am sure this is probably a simple maths thing but it just keeps eluding me. Any help you can offer would be great.

Thanks