Question

You Finally got that red rider BB gun you always wanted! After your first semseter of physics, however, you are a little suspicious of the advertised muzzle velocity. Throwing all caution to the wind, you point the gun at a wall 3.0 m away and fire. The pellet strikes the wall .210m below the level of the barrel. What isis the initial velocity of the pellet?

Answer 1

Using 2nd kinematic equation in vertical direction:

h = V0y*t + (1/2)*ay*t^2

ay = -g = -9.81 m/sec^2

V0y = Initial vertical velocity = 0 m/sec, since gun is pointed at wall, So initial velocity is only in horizontal direction

h = vertical distance traveled by pellet = -0.210 m

So,

-0.210 = 0*t + (1/2)*(-9.81)*t^2

t = sqrt (2*0.210/9.81)

t = 0.207 sec

Now Range in horizontal direction is given by:

R = V0x*t

V0x = Initial horizontal velocity = initial velocity of pellet = V0

R = 3.0 m

So,

V0x = V0 = R/t = 3.0/0.207

V0 = 14.5 m/sec

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