Question

A spotlight on the ground is shining on a wall 12m away. If a woman 2m tall walks from the spotlight toward the building at a speed of 1.2m/s, how fast is the length of her shadow on the building decreasing when she is 6m from the building?

Answer 1

Shadow length L can be written as:

2/x = L/12
where x is the distance the woman is from the spotlight.
So:

L = 24/x

dL/dx = -24/x^2

When she is 6m from the BUILDING, she's 18m from the light,
and:

dL/dx = -24/(18^2)

dL/dt = dL/dx * dx/dt = -24/(18^2) * 1.2 m/s = -0.088 m/s

It's shrinking at 8.8 cm/sec.