Question

A ladder 10ft long rests against a vertical wall. If the bottom of the ladder slides away from the wall at a speed of 2ft/s, how fast is the angle between the top of the ladder and the wall changing when the angle is π4 rad?

Answer 1

Answer:

Let x be the distance of the foot of the ladder from the wall.

x = 10 * sin theta     where theta is the angle between the wall and the ladder

dx/dt = 10 cos theta * d theta / dt

so d theta / dt = (dx / dt) / (10 cos theta)

Since pi/4 rad = 45 deg then cos 45 = .707 and dx / dt = 2 ft/sec

d theta / dt = 2 / (10 * .707) = .283 rad / sec = .283 * 180 / pi = 16.2 deg / sec