Calculus 1 work problem. 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

This is a fairly typical example of related rates questions (another version is a ladder sliding down a wall). Since they don't ask about angles, we need only the Pythagorean Theorem (well, at first):

A² + B² = C²

Plug in the two values you have for distance:

500² + 600² = C²                 and solve for C:

781.025 = C

Now, derive implicitly:

2A dA + 2B dB = 2C dC

     dT         dT          dT

2(500)( 0 ) + 2(600)(140) = 2(781.025) dC            Because we now know all 3 sides, and the A value never

                                                           dT            changes.

168,000 = 1562.05 dC

                            dT

197.551 = dC

                dT