Two cars are moving away from an intersection along roads that make a 90 degree angle. The first car is 100 feet from the intersection and is travelling at a rate of 30 ft/s. The second care is 150 feet away from the intersection and is travelling at a rate of 40ft/s. Find the rate of change of the distance between the cars after one second.

Question

Mathematics

Jaxson Chang

12 January, 08:13

Two cars are moving away from an intersection along roads that make a 90 degree angle. The first car is 100 feet from the intersection and is travelling at a rate of 30 ft/s. The second care is 150 feet away from the intersection and is travelling at a rate of 40ft/s. Find the rate of change of the distance between the cars after one second.

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Natalia Bridges · Answer 1

D = sqrt (x^2 + y^2); where x = 100 ft, y = 150 ft, dx/dt = 30ft/s, dy/dt = 40ft/s

After one second, x = 130 ft, y = 190 ft

ds/dt = (2x dx/dt + 2y dy/dt) / (2sqrt (x^2 + y^2) = (2 (130) (30) + 2 (190) (40)) / 2sqrt (130^2 + 190^2) = (7,800 + 15,200) / 2sqrt (16,900 + 36,100) = 23,000 / 2sqrt (53,000) = 49.95 ft/s

Therefore, the rate of change of the distance between the cars after one second is approximately 50 ft/s.