1) A criminal steals a car and roars onto the highway at 100km/hr heading for th
ID: 1405311 • Letter: 1
Question
1) A criminal steals a car and roars onto the highway at 100km/hr heading for the border 300km away. If the cops get to the highway onramp 30 minutes later, what must their minmum average speed be in order to catch the criminal before he reaches the border?
2) Two cars are racing down a straight track with length L. Car A travels the entire distance at a constant velocity v. Car B covers the first third of the track at a speed 0.5v and the final third of the track at a speed at a speed 1.5v
a) Explain which car, if either, reaches the end of the track in less time, and justify your answer qualitatively (without using equations).
b) Justify your answer about which car, if either, finishes the race in less time quantitatively (with appropriate equations).
c) Explain how your equations in part (b) re-express your reasoning in part (a). Do not simply refer to any fina results of your caculations, but instead indicate how terms in your equations correspond to concepts in your qualitative explanation.
Explanation / Answer
1)
Criminal reaches border in 300/100 = 3 hour
Cops should reach there is 2.5 hours
Average spped of cops = distance/time
= 300/2.5
= 120 km/hr
2)
a)
Since 2nd car increases his speed by 50% for final third and increases his speedby 50% for 1st 3rd. I will think that both car reached in same amount of time.
b)
For 1st car,
time taken, t = L/v
For 2nd car:
t = (L/3)/0.5v + (L/3)/v + (L/3)/1.5v
= L/1.5v +L/3v + L/4.5v
=L/v (1/1.5 +1/3 +1/4.5)
=1.22 L/v
1st car takes less time
c)
In part a I was wrong.
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