Calculus 1 - Related Rates Question

Question

A 17 foot ladder is leaning against a wall. If the top slips down the wall at a rate of 3 ft/s, how fast will the foot be moving away from the wall when the top is 13 feet above the ground?

Answer: ____ ft/s

Answer 1

x² + y² = h² h=17 y=13 x=2√30 dy/dt=-3

x² + y² = 17²

2x dx/dt + 2y dy/dt = 0

2(2√30) dx/dt + 2(13)(-3) = 0

4√30 dx/dt - 78 = 0

dx/dt = 78/4√30 = 3.56 The ladder is moving away from the wall at a rate of 3.56 feet/second.