KinematicsHard
Question
A gun is set up in such a way that the muzzle is at ground level as in figure. The hoop A is located at a horizontal distance 40 m from the muzzle and is 50 m above the ground level. Shell if 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 if its fired is 55 m/s
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 after it is 45 m / s if the shell is to pass through both the hoops
Solution
As given horizontal velocity = 40m/s
u cos θ × t = 40; t = 1 sec
At t = 1, height = 50 m
∴ 50 = u sin θ × 1 - 1 / 2 × g × 1 ⇒ u sin θ = 55
∴ Initial vertical component = u sin θ = 55 m/s
As hoop is on same height of the trajectory.
So by symmetry x will be 40 m.
u cos θ × t = 40; t = 1 sec
At t = 1, height = 50 m
∴ 50 = u sin θ × 1 - 1 / 2 × g × 1 ⇒ u sin θ = 55
∴ Initial vertical component = u sin θ = 55 m/s
As hoop is on same height of the trajectory.
So by symmetry x will be 40 m.
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