Question

A man 2m tall walks away at a rate of 4m/min from the source of light 6m height from the ground how fast is the length of his shadow changing

Answer 1

Answer:

Draw a diagram showing the light source and man.

Let d be distance between light source and man and s be length of shadow.

From diagram, we can see that we have two similar triangles.

Smaller triangle has base = s and height = 2

Larger triangle has base = d+s and height = 6

From properties of similar triangless/2 = (d+s)/6

From properties of similar triangless/2 = (d+s)/66s

= 2d + 2s4s

= 2ds

= (1/2) dds/dt

= (1/2) d(d)/dt

Man walks at a speed of 4 m/min

dd/dt = 4 m/min

ds/dt = (1/2) * 4

ds/dt = 2

Shadow is growing at rate of 2 m/min