Question

You are walking away from a 4.5 m tall lamp post at a rate of 6 km/hr. If you are 1.5 m tall, how fast is the length of your shadow increasing?

Answer 1

The length of your shadow is decreasing at a rate of 2 km/hr.

Step-by-step explanation:

To determine how fast the length of your shadow is increasing, we can use similar triangles. Let's assume the length of your shadow is S and the distance between you and the lamp post is D. The height of the lamp post is H and your height is h. Since the triangles formed by the lamp post and your shadow are similar, we can write the following equation:

(h/S) = (H/D)

To find the rate at which the length of your shadow is increasing, we can differentiate both sides of the equation with respect to time:

(dS/dt) = (h/H) * (dD/dt)

Substituting the given values, we have:

(dS/dt) = (1.5/4.5) * (-6 km/hr)

(dS/dt) = -2 km/hr

Therefore, the length of your shadow is decreasing at a rate of 2 km/hr.