A man 2m tall walks at the rate of 5/3 m/s towards a street pole which is 16/3 m tall. At what rate the top of his shadoes is moving when he is 10/3 m from the base of the pole
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it seems data 10/3 m from the base of the pole is not needed
As you draw the diagram with shadow length as s and b is the distance between the man and pole, by similar triangles,
s /(s+b) = 2/(16/3) = 3/8
Or 5 s = 3 b
Or s = 3/5 * b
Differentiating w.r.t time you get ds/dt = 3/5 * db/dt
But db/dt = 5/3 m/s
Plug and you get ds/dt = 1 m/s
As you draw the diagram with shadow length as s and b is the distance between the man and pole, by similar triangles,
s /(s+b) = 2/(16/3) = 3/8
Or 5 s = 3 b
Or s = 3/5 * b
Differentiating w.r.t time you get ds/dt = 3/5 * db/dt
But db/dt = 5/3 m/s
Plug and you get ds/dt = 1 m/s
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