A gun is set up in such a wat that the muzzle is at around level as in figure. The hoop A is located at a horizontal distance 40m from the muzzle and is 50m above the ground level. Shell is fired with initial horizontal component of velocity as `40 m//s`. Which of the following is `//`are correct?

Options

A. The vertical component of velocity of the shell just after it is fired is `55 m//s`, if the shell has to pass through the hoop a.
B. The shell will pass through both the hoops if `x=40 m`
C. The shell will pass through both the hoops if `x=20 m`
D. The vertical component of velocity of the shell just after it is fired is `45 m//s`, if the shell is to pass through both the hoops

Answer

A, B

Explanation

As given horizontal velocity `=40 m//s`
`u cos theta xxt=40, t=1` sec
at `t=1`, height `=50 m`
`:. 50=u sin theta xx1-1//2xxgxx1rArr u sin theta=55`
`:.` Initial vertical component `=u sin theta=55 m//s`
As hoop is on same height of the trajectory. So by symmetry x will be 40 m.