Question

A ladder 10 ft long rests against a vertical wall. If the bottom of the ladder slides away from the wall at a rate of 0.9 ft/s, how fast is the angle between the ladder and the ground changing when the bottom of the ladder is 6 ft from the wall? (That is, find the angle's rate of change when the bottom of the ladder is 6 ft from the wall.)

Answer 1

Answer:

Explanation:

Length of the ladder, L = 10 ft

dx / dt = 0.9 ft/s

x = 6 ft

Let the angle is θ.

According to the diagram

x = L cosθ

Differentiate both sides with respect to t

$\frac{dx}{dt} = - L Sin\theta \frac{d\theta }{dt}$

At,  x = 6 ft

Sin θ = 0.8

So,

0.9 = -  10 x 0.8 x dθ/dt

dθ/dt = - 0.1125 rad/s