A horizontal rifle is fired at a bull's-eye. The muzzle speed of the bullet is 795 m/s. The barrel is pointed directly at the center of the bull's-eye, but the bullet strikes the target 0.042 m below the center. What is the horizontal distance between the end of the rifle and the bull's-eye?

It reaches the target T = X/795 seconds.

Thet time T is the time it takes the bullet to fall H = 0.042 m.
T = sqrt(2H/g)= 0.0926 s

X = 795 T = ___ meters

A rifle shoots a 4.50g bullet out of its barrel. The bullet has a muzzle velocity of 960m/s just as it leaves the barrel.

To find the horizontal distance between the end of the rifle and the bull's-eye, we need to determine the time it takes for the bullet to travel from the end of the rifle to the target.

First, let's determine the time it takes for the bullet to reach its maximum height. Since the vertical motion is affected by gravity, we can use the kinematic equation for vertical displacement:

Δy = v₀y * t + (1/2) * a * t²

Where:
Δy = vertical displacement of the bullet (0.042 m below the center)
v₀y = initial vertical velocity of the bullet (0 m/s, since the bullet starts horizontally)
t = time taken
a = acceleration due to gravity (-9.8 m/s²)

Since the bullet reaches its maximum height, the final vertical displacement is zero. Thus, the equation becomes:

0 = 0 * t + (1/2) * (-9.8) * t²

This simplifies to:

-4.9t² = 0

Solving for t, we find:

t = 0 seconds

This tells us that the bullet takes 0 seconds to reach its maximum height, which makes sense because it was fired horizontally.

Now, let's determine the total horizontal distance from the end of the rifle to the bull's-eye. Since the horizontal motion is unaffected by gravity, the horizontal velocity remains constant.

We know that the initial horizontal velocity (v₀x) is equal to the muzzle velocity of the bullet (795 m/s). We also know that the time taken (t) is 0 seconds since the bullet traveled horizontally. Therefore, we can use the equation:

Δx = v₀x * t

Substituting in the values, we get:

Δx = 795 m/s * 0 s
Δx = 0 m

This means that the horizontal distance between the end of the rifle and the bull's-eye is 0 meters.