A man of height 1.8 metre is moving away from a lamp post at the rate of 1.2 m/sec . If the height of the lamp post be 4.5 metre , then the rate at which the shadow of the man is lengthening is
A
0.4m/sec
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B
0.8m/sec
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C
1.2m/sec
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D
None of these
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Solution
The correct option is B0.8m/sec
1st second
height of man =1.8m
height of the lamp=4.5m
4.51.8=52
2nd second
height of man =1.8m
height of the lamp=4.5m
4.51.8=4.2+xx
⇒4.5x=7.56+1.8x
⇒4.5x−1.8x=7.56
⇒2.7x=7.56
⇒x=7.562.7=2.8
3rd second
height of man=1.8m
height of the lamp=4.5m
4.51.8=5.4+xx
⇒4.5x=9.72+1.8x
⇒4.5x−1.8x=9.72
⇒2.7x=9.72
⇒x=9.722.7=3.6
1st second, length of the shadow of man =2m
2nd second, length of the shadow of man =2.8m
3rd second, length of the shadow of man =3.6m
The length of the shadow of man =2.8−2=3.6−2.8=0.8ms−1