Question

A ladder 10 meters long rests with one end against a vertical wall, the other end on the floor. The lower end moves away from the wall at the rate of 2 metres/minute. The rate at which the upper end falls when its base is 6 metres away from the wall, is –

• A. –3 metres/min
• B. –2/3 metres/min
• C. –3/2 metres/min
• D. None of these

Answer 1

Answer: (C)

–3/2 metres/min

Answer 2

Let at time t, the lowers end P of ladder PQ be at a distance x metres from the wall and the upper end Q be at height y from the ground. Then, x² + y² = 10²

It is given that $\frac{dx}{dt}$ = 2.

We have to find $\frac{dy}{dt}$ when x = 6

On putting x = 6 in x² + y² = 10², we get y = 8

Now,

x² + y² = 10²

̃ 2x $\frac{dx}{dt}$ + 2y $\frac{dy}{dt}$ = 0

̃ 6 × 2 + 8 × $\frac{dy}{dt}$ = 0

$\left\{ Puttingx = 6,y = 8and\frac{dx}{dt} = 2 \right\}$

̃ $\frac{dy}{dt}$ = – $\frac{3}{2}$ metres/min.

Hence (3) is the correct answer.