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A man of height h walks in a straight pa...

A man of height h walks in a straight path towards a lamp post of height H with uniform velocity u. Then the velocity of the edge of the shadow on the ground will be :

A

A)`(hv)/((H- h ))`

B

B)`(Hu )/((H+ h ))`

C

C)`((H- h ))/( Hu)`

D

D)'((H + h))/( Hu )`

Text Solution

Verified by Experts

The correct Answer is:
A
Let is same time `t,` distance covered by man and edge of image be respectively x and y.
`tan theta = ( H - h )/(x) = (H)/(x + y)`
`implies H x = Hx + Hy - hx + hy`

`implies (x)/(y) = ((H - h ))/( h) " "...(i)`
Now `x = ut `
and `y = vt`
`implies (x)(y) = (u)/(v) " "...(2)`
Hence, `(u)/(v) = ((H - h ))/(h) `
`impliesv = ( hv )/(( H - h ))`
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