Passing speed

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Passing speed

Postby barnamah » Fri 18 March, 2011 17:51

Exercise 73
Passing speed
An automobile 20 feet long overtakes a truck 40 feet long that is traveling at 50 mile/h. At what constant speed must automobile travel in order to pass the truck in 5 seconds?
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Re: Passing speed

Postby ChangBroot » Sat 19 March, 2011 17:57

Since this problem involves relative velocity, then the Automobile's speed plus 50 mi/hr will give us the answer. To simplify this problem, we assume that the truck is at rest, and we want to find the constant speed at which the Automobile passes 60 ft(40 ft long truck + 20 ft automobile). Also, since the it's constant speed, the acceleration is zero. Therefore, we simply apply `v = d/t`.

d = 60ft = 0.0113636 miles

`t = 5s((1hr)/(3600s))`= `1.389*10^-3` hours

`v = (0.0113636mi) / (1.389*10^-3 h) = (8.18mi)/(hr)`

Since at the beginning we assumed the truck was at rest, now we add the truck's speed to the Automobile's speed

`V = (8.18 mi)/(hr) + (50mi)/(hr) = (58.2mi)/(hr)`

Therefore, the constant speed of the automobile should be 58.2 mi/hr.
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