A water hose pipe of cross-sectional area `5cm^(2)` is used to fill a tank of `120L`. It has been observed that it takes 2 min to fill the tank. Now, a nozzel with an opening of cross-sectional area `1cm^(2)` is attached to the hose. The nozzel is held so that water is projected horizontally from a point 1m above the ground. The horizontal distance over which the water can be projected is (Take `g=10m//s^(2))`.

Options

A. `3m`
B. `8m`
C. `4.47m`
D. `8.64 m`

Answer

C

Explanation

Volume flow rate `=av=(V)/(t)`
`:. v_(1)=(V)/(A_(1) t)=(120xx10^(-3))/(5xx10^(-4)xx2xx60)`
Now, `A_(1)v_(1)=A_(2)v_(2)`
`A_(2)` is `(1)/(5)`th of `A_(1)`.
Hence, `v_(2)` is five times of `v_(1)` or `10m//s`
`t_(0)=sqrt((2h)/(g))=sqrt((2xx1)/(10))`
`=0.447s`
`R=v_(2)t_(0)=4.47m`.