Question

A ladder 5 m in length is resting against vertical wall. The bottom of the ladder is pulled along the ground away from the wall at the rate of 1.5 m/sec. The length of the highest point of the ladder when the foot of the ladder is 4.0 m away from the wall decreases at the rate of –

• A. 2 m/sec
• B. 3 m/sec
• C. 2.5 m/sec
• D. 1.5 m/sec

Answer 1

Answer: (A)

2 m/sec

Answer 2

x² + y² = 25 Ž 2x $\frac{dx}{dt}$ + 2y $\frac{dy}{dt}$ = 0

but $\frac{dx}{dt}$ = 1.5 m/sec.

\ 2(x) (1.5) + 2(y) $\frac{dy}{dt}$ = 0 Ž $\frac{dy}{dt}$ = – $\frac{1.5x}{y}$

When x = 4, y = 3.

\ $\frac{dy}{dt}$ = – $\frac{1.5 \times 4}{3}$= – 2m/sec.

\ Height of the wall is decreasing at the rate of 2m/sec.