An automobile traveling at a rate of 30 ft/sec is approaching an intersection. W

Question

An automobile traveling at a rate of 30 ft/sec is approaching an intersection. When it is exactly 120 ft from the intersection, a truck traveling at a rate of 40 ft/sec crosses the intersection. Assume that the automobile and truck are traveling on roads which are perprendicular. What is the minimum distance between the car and truck (after the truck crosses the intersection)? At what time (after the truck crosses the intersection) does this occur?

Can you please answer those two questions with an explination of how you did it and why you used the process you did?

Explanation / Answer

Automobile's Distance, A = 120 ft.
Automobile's Speed, dA/dt = - 30 ft./sec. (Negative because the distance is decreasing)
Truck's Distance = T
Truck's Speed, dT/dt = 40 ft./sec.
Time, t = 2 secs.
Distance Between = d

Find dd/dt:

Since the automobile has traveled some distance in 2 secs.,

A = A - [(dA/dt)]t (Absolute value because the direction here is irrelevant)
A = 120 - (30)(2)
A = 120 - 60
A = 60

T = (dT/dt)t
T = (40)(2)
T = 80

d

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