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 at 19.7 m/s. From one direction, two trucks arrive at the dump every four minutes. A bicyclist is also traveling toward the dump, at 4.47 m/s.
(a) With what frequency do the trucks pass him?
(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, road hogging trucks whiz past him now?

Explanation / Answer

First, find the spacing of the trucks.

2 every 4 mins = 1 every 2 minutes.
They are travelling at 19.7 m/sec., so (19.7 x 60) they travel 1182m per minute. Multiply by 2, and they are 2364m apart on the road.
Now, if you subtract the cyclist's velocity from the truck's velocity, (19.7 - 4.47) = 15.23m/sec. It is then as though the bicycle is stationary, and the trucks are passing at 15.23 m/sec. 15.23 x 60 = 913.8 metres/ min.
The trucks are 2364 metres apart.

So, (2364/913.8) = 2.587 mins, the time between trucks passing the cyclist.

b)

now cyclist's speed = 1.56 m/s

then (19.7 - 1.56), the bicycle is stationary, and the trucks are passing at 18.14 m/sec = 18.14*60 = 1088.4 meters/min

distance between trucks is 2364 meters.

so, (2364/1088.4) = 2.1719 mins,the new time between trucks passing the cyclist.

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