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
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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
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