Aspotlight on the ground is shining on a wall 24m away. if a woman 2m tall walks from the spotlight toward the building at a speed of 0.6m/s, how fast is the length of her shadow on the building decreasing when she is 2m from the building?

Explanation:

It is given that,

Distance between the spotlight and the wall, y = 24 m

Height of the woman, h = 2 m

The woman walks toward the building at the rate of 0.6 m/s,

In the attached figure, triangle ABC and MNC are similar. So,

............(1)

When she is 2 meters from the building. So x = 24-2 = 22 m

Differentiating equation (1) i.e.

So, her shadow is decreasing at the rate of 0.059 m/s. Hence, this is the required solution.                                

does anyone know or what?