Calc Please Help

Question

A balloon rising from the ground at 140ft/min is tracked by a rangefinder at point a, located 500ft from the point of liftoff. Find the rate at which the distance between the range finder and the balloon is changing when the balloon is 600ft above the ground.

Answer 1

Y is the distance from the balloon from the ground.

By pythagorean theorem , the distance from the rangefinder
to the balloon is

sqrt( y^2 + 250000) = F(y)


dF/dt = 1/2( y^2 + 250000) ^(-1/2) ( 2y) (dy/dt)


F'(600) =
1/2( 600^2 + 250000) ^(-1/2) ( 2*600) ( 140)

= (1/2)(1200)(140) / sqrt( 600^2 + 250000)

= 84000 / sqrt( 360000 + 250000)

= 84000 / sqrt(610000)

107.551 ft/sec