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

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Answer 1 · 2015-04-26T01:03:04

Let the Height of the girl's shadow on the wall be #h#
and the distance the girl is from the light be #w#

We are asked for #(dh)/(dt) " where " t " is a measure of time"#

We are given #(dw)/(dt) = -60 " cm/sec"#

and using the diagram below we can determine #(dh)/(dw)#
enter image source here

#h = (6xx10^4)/w#

#rarr (dh)/(dw) = - (6x10^4)/(w^2)#

#(dh)/(dt) = (dh)/(dw)*(dw)/(dt)#

#= ((-6xx10^4)/(w^2)) * (-6x10)#

#=(36xx10^5)/w^2 " (cm/sec)"#

When #w=150#

#(dh)/(dt) = (36xx10^5)/150^2 " (cm/sec)"#

#= (36xx10^3)/(225) " (cm/sec)#

#= 160 " cm/sec"#