Question

A man of height 1.1 meters walk away from a 5− meter lamppost at a speed of 2.6 m/s. Find the rate at which his shadow is increasing in length. Rate = m/sec (Give your answer upto 3 decimal places.)

Answer 1

The rate at which the man's shadow is increasing in length is approximately -0.572 m/s.

Step-by-step explanation:

To find the rate at which the shadow is increasing in length, we can use similar triangles. Let's denote the length of the shadow as S and the distance between the man and the lamppost as D.

Since the height of the man is 1.1 meters and the length of the lamppost is 5 meters, we have:

S / D = 1.1 / 5

Solving for S, we get:

S = (1.1 / 5) * D

Now, we can find the rate at which the shadow is increasing by taking the derivative with respect to time:

dS/dt = (1.1 / 5) * dD/dt

Since the man is walking away from the lamppost at a speed of 2.6 m/s, we have:

dD/dt = -2.6 m/s

Substituting the values, we get:

dS/dt = (1.1 / 5) * (-2.6) m/s

Simplifying, we find that the rate at which the shadow is increasing is approximately -0.572 m/s.