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A man of height 1.8m walks away from a lamp at a height of 6m. if the man’s speed is 7m/s , the speed in m/s at which the tip of the shadow moves is A)5m/s B)7m/s C)10m/s D)17m/s

A man of height 1.8m walks away from a lamp at a height of 6m. if the man’s speed is 7m/s  , the speed in m/s at which the tip of the shadow moves  is 
A)5m/s
B)7m/s
C)10m/s
D)17m/s

Grade:12th Pass

1 Answers

Vikas TU
14149 Points
7 years ago
The shadow triangle and the men’s triangle with lamp would be simlar.
Hence let x be the distance of tip of the shadow from man and y be the distance of man from the lamp at any instant.
Then,
from similar triangles we get,
1.8/x = 6(x+y)
or
7x = 3y........................................................(1)
 
Now from distance – speed formulae:
for man,
7 = y/t => t = y/7 seconds.
for shadow,
v = (x+y)/t => t = (x+y)/v
now time would be same for both therfore,
v = 7x/y + 7 
from eqn. (1) we get,
v = 3 + 7 => 10 m/s.

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