A small 1.0 kg mass is launched form the top of the cliff with speed V at an angle of `30^(@)` above the horizontal. When the mass reaches the ground, its velocity is directieon at `45^(@)` below the horizontal. Which one of the following choices is the magnitude of the total impulse that was imparted to the mass durints its flight ? Ignore air resistance.

Options

A. `1/2 (sqrt(3)+1)V`
B. `((sqrt(3))/(sqrt(2))-1)V`
C. `1/2(sqrt(3/2)+1)V`
D. `sqrt(3/2) ((sqrt(2)+1))/((sqrt(2)-1)) V `

Answer

A

Explanation

`v cos 30^(@)=v_(1)cos45^(@)`
`v_(1)=(vsqrt(3))/(sqrt(2))` ltvegt `J=p_(fy)-p_(iy)=mv_(1)sin45^(@)+mv sin 30^(@)`
`=m((vsqrt(3))/(sqrt(2))xx1/(sqrt(2))+(1u)/2) = mv((sqrt(3)+1)/2)`