In the accompanying figure. Line l passes through the origin and the point (2, 4). Line m (not shown) is perpendicular to line l at (2, 4). Line m intersects the x-axis at which point?

Options

A. 10m
B. 7.1 m
C. 5 m
D. 3.2 m

Answer

D

Explanation

Let the velocity at point B is `V_(B)`.
Form conservation of total mechanical energy.
`mg[h-L sinalpha]=1/2mv_(B)^(2)`
`rArr v_(B)^(2)=2g(h-Lsinalpha)=2g(10 -2 xx 1/2)`
`rArr v_(B)^(2)=18g`
Now, let maximum height attained by water stream, be (H).
`therefore H=Lsintheta+(v_(B)^(2)sin^(2)alpha)/(2g)`
`rArr H=2 xx 1/2 + (18g(1/2)^(2))/(2g)=1+18/2=3.25 m`