A man 160 cm tall walks away from a source of light situated at the top of the pole 6m high at the rate of 1.1 m/sec. How fast is the length of the shadow increasing when he is 1m away from the pole.
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Let the distance of the man from source of light be x
the distance of length of shadow from the man be y
Seeing figure attached, it is clear that triangles ABC and PQC are similar, thus, we can write the ratio of sides as
AB/BC = PQ/QC
600/(x + y) = 160/y
600y = 160x + 160y
160x = 440y
y = 4/11 x...(1)
Now, to get the rate of change of shadow, we want dy/dt
Differentiating (1) wrt to t we get
dy/dt = 4/11 dx/dt
As the man walks at 1.1 m/s or 110 cm/s i.e dx/dt, we have
dy/dt = 4/11 (110) = 40 cm/s [constant]
So, the length of the shadow is moving at 0.4 m/s and iis independent of the man's position from the light.
the distance of length of shadow from the man be y
Seeing figure attached, it is clear that triangles ABC and PQC are similar, thus, we can write the ratio of sides as
AB/BC = PQ/QC
600/(x + y) = 160/y
600y = 160x + 160y
160x = 440y
y = 4/11 x...(1)
Now, to get the rate of change of shadow, we want dy/dt
Differentiating (1) wrt to t we get
dy/dt = 4/11 dx/dt
As the man walks at 1.1 m/s or 110 cm/s i.e dx/dt, we have
dy/dt = 4/11 (110) = 40 cm/s [constant]
So, the length of the shadow is moving at 0.4 m/s and iis independent of the man's position from the light.
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