SOLUTION: A car traveling goes through an intersection. The car is traveling north at a constant speed of 40 miles per hour. Fifteen minutes later, a truck goes through the same intersection
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Question 462829: A car traveling goes through an intersection. The car is traveling north at a constant speed of 40 miles per hour. Fifteen minutes later, a truck goes through the same intersection. The truck is traveling east at a constant speed on 50 miles per hour. Find the rate at which the distance between them is changing 1 hour after the car goes through the intersection.
dr/dt= x(dx/dt)/r
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
At time t = 15 minutes, we can say that the car's position is 10 miles north (since it would have traveled 10 miles going at 40 mph). We can let X and Y denote the positions of the truck and car (since the truck and car are traveling east and north, respectively). Then,
Also, by the Pythagorean theorem,
^2 + (50t)^2} = \sqrt{4100t^2 + 80t + 100})
where Z denotes the distance between the car and truck. Differentiating both sides,
^{-\frac{1}{2}} (8200t + 80))
At time t = 1 hour, dZ/dt is approximately 63.28 miles per hour.
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