| 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, then find the length of her shadow after 4 s. |
A) 8 m
B) 1.6 m
C) 2.8 m
D) 2 m
Correct Answer: B
Solution :
| Let length of shadow = DE = x m |
| BD = Distance covered by the girl in 4 s |
 |
| \[=1.2\times 4=4.8\text{ }m\] |
| Also, in \[\Delta ABE\] and \[\Delta CDE\] |
| and \[\angle B=\angle D\] |
| \[\Rightarrow \] \[\angle A=\angle C\]and \[\angle E=\angle E\] |
| \[\therefore \] \[\Delta ABE=\Delta CDE\] |
| \[\therefore \]\[\frac{BE}{DE}=\frac{AB}{CD}\]\[\Rightarrow \]\[\frac{4.8+x}{x}=\frac{3.6}{0.9}\] |
| \[\Rightarrow \] \[4.8+x=4x\]\[\Rightarrow \]\[x=1.6\,m\] |
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