Homework Help: calculus

Posted by nesri on Tuesday, October 5, 2010 at 8:06am.

A shark, looking for dinner, is swimming parallel to a straight beach and is 90 meters offshore. The shark is swimming at a constant speed of 30 meter per second. At time t = 0, the shark is directly opposite a lifeguard station. How fast is the shark moving away from the lifeguard station when the distance between them is 150 meters?

calculus - Reiny, Tuesday, October 5, 2010 at 9:36am
make a diagram, you will have a right-angled triangle
let the horizontal distance covered by the shark since t=0 be x m , and
let the distance between the shark and the lifeguard be y m
x^ + 90^2 = y^2
2x(dx/dt) + 0 = 2y(dy/dt)

when y = 150
x^2 + 90^2 = 150^2
x = √14400 = 120

dy/dt = 2x(dx/dt)/(2y)
= 2(120)(30)/300
= 24 m/sec

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