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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?

Answer 1

Paisley Johnson

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)#

#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"#

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Answer 2

Ezra Adams

When the girl is 1.5 m from the light, her shadow size decreases. This is because she is closer to the light source, causing her shadow to become smaller in proportion to her height.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.