Aiming with a gun - Motion in two dimensions
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A high-powered rifle fires a bullet with a muzzle speed of 1.00 km/s. The gun is pointed horizontally at a large bull's eye target - a set of concentric rings - 200 m away.
(a) How far below the extended axis of the rifle barrel does a bullet hit the target?
Since the horizontal and vertical components of the velocity of a projectile behave independent of each other, we use the following two equations to describe those components:
Eq 1 vx = v0x
where v0x is the initial horizontal velocity and vx is the horizontal velocity at any time. (Notice that the horizontal velocity does not depend on time.)
Eq 2 vy = v0y + g t
Where v0y is the initial vertical velocity and vy is the vertical velocity at any time. (Notice that the vertical velocity does depend on time since g = -9.8 m/s2)
We have v0x = 1km/s = 1000 m/s
One can also find relationships for the distance travelled in each direction. Equations giving these ...
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