Question

Given a 15-foot ladder leaning against a wall, with the base being pulled away at a rate of 0.5 ft/sec, find the rate at which the height of the ladder (where it hits the wall) is changing when the base is 9 ft from the wall.

a. 0.25 ft/sec
b. 0.3 ft/sec
c. 0.4 ft/sec
d. 0.5 ft/sec

Answer 1

The rate at which the height of the ladder is changing when the base is 9 ft from the wall is 0.25 ft/sec.

Step-by-step explanation:

To find the rate at which the height of the ladder is changing, we can use related rates. Let h represent the height of the ladder and x represent the distance of the base from the wall.

By using similar triangles, we have h/x = 15/9.

Differentiating both sides with respect to time t, we get (dh/dt)/(dx/dt) = 15/9.

Plugging in the given values, we have (dh/dt)/(0.5) = 15/9. Solving for dh/dt, we get dh/dt = 0.25 ft/sec.