On a Saturday morning, pickup trucks and sport utility vehicles carrying garbage

Question

On a Saturday morning, pickup trucks and sport utility vehicles carrying garbage to the town dump form a nearly steady procession on a country road, all traveling at21.8 m/s. From one direction, two trucks arrive at the dump every two minutes. A bicyclist is also traveling toward the dump, at 4.12 m/s.

(a) With what frequency do the trucks pass him?
?min-1
(b) A hill does not slow down the trucks, but makes the out-of-shape cyclist's speed drop to 1.56 m/s. How often do noisy, smelly, inefficient, garbage-dipping, roadhogging trucks whiz past him now?
? min-1

Explanation / Answer

a) find the spacing of the trucks. 2 every 2 mins = 1 every 1 minutes.
They are travelling at 21.8 m/sec., so (21.8 x 60) they travel 1308 per minute. Multiply by 1min, and they are 1308 m apart on the road.

Now, if you subtract the cyclist's velocity from the truck's velocity, (21.8 - 4.12) = 17.68 m/sec. It is then as though the bicycle is stationary, and the trucks are passing at 17.68 m/sec. 17.68 x 60 = 1060.8 metres/ min.
The trucks are 1308 metres apart. So, (1308/1060.8) = 1.233 mins, the time between trucks passing the cyclist. => frequency = 1/1.233 = 0.811 min-1

b) For the second one. Just substitute the new cyclist rate.

If you subtract the cyclist's velocity from the truck's velocity, (21.8 - 1.56 ) = 20.24 m/sec. It is then as though the bicycle is stationary, and the trucks are passing at 20.24 m/sec. 20.24 x 60 = 1214.4 metres/ min.

The trucks are 1308 metres apart. So, (1308/1214.4) = 1.077 mins, the time between trucks passing the cyclist. => frequency = 1/1.077 = 0.928 min-1

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