A spotlight 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 0.8m/s, how fast is the length of her shadow

Question

A spotlight on the ground is shining on a wall  away. If a woman  tall walks from the spotlight toward the building at a speed of  how fast is the length of her shadow on the building changing when she is  from the building?

Answer 1

Draw a figure

Let y(t)=height of shadow at time t and x(t) be the woman's distance from the light at time t.

y(t)=12 x(t)

dy/dt = 12 dx/dt = 12*.8 = 7.2 m/s

Please note that as long as the woman walks at a constant speed the height of the shadow increases at a constant speed, irrespective of the woman's position!