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Q.

A girl of height 90 cm is walking away from the base of a lamp post at a speed of 1.2 m/s. If the lamp is 3.6 m above the ground, find the length of her shadow after 4 seconds.


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a

140 cm

b

150 cm

c

160 cm

d

170 cm 

answer is C.

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Detailed Solution

Concept: Draw a diagram of the given data to get an idea of what we need to find. Show that the triangles formed in the diagram are congruent, and thus find the girl's shadow.
Consider the girl of height is at point Question Imageon the ground from the lamp post after 4 seconds.
imageQuestion ImageAssume that the length of the shadow of the girl be Question Image when she is at position D.
Question ImageIn Question Image and Question Image,
Question ImageQuestion Image (Common)
Thus, Question Image (AA similarity)
Question Image(Corresponding sides are proportional)
Question ImageQuestion ImageQuestion ImageQuestion ImageQuestion ImageQuestion ImageSo, length of her shadow after Question Image seconds is Question Image cm.
​Hence, the correct answer is option 3) 160cm.
 
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