A girl of height 120 cm is walking towards a light on the ground at a speed of 0.6 m/s. Her shadow is being cast on a wall behind her that is 5 m from the light.

Question

How is the size of her shadow changing when she is 1.5 m from the light?

Answer 1

draw a diagram. Using similar triangles, if her shadow has height h when she is x cm from the light, then

h/500 = 120/x
or,
hx = 60000
so,
h dx/dt + x dh/dt = 0

Now, find h when x = 150, and you know that dx/dt = -60 cm/s; you can then find dh/dt