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?
73.06
To find the horizontal distance between the end of the rifle and the bull's-eye, we can use the equation of motion in the horizontal direction.
First, we need to determine the time it takes for the bullet to reach the bull's-eye. To do this, we can find the time of flight, which is the total time the bullet is in the air.
Using the equation of motion for vertical motion, we can determine the time of flight (t) using the equation:
0.042 m = (1/2) * g * t^2 (where g is the acceleration due to gravity, which is approximately 9.8 m/s^2)
Solving for t, we get:
0.042 m = (1/2) * 9.8 m/s^2 * t^2
0.084 m = 4.9 m/s^2 * t^2
t^2 = (0.084 m) / (4.9 m/s^2)
t^2 = 0.01714 s^2
t ≈ √(0.01714) s
t ≈ 0.131 s
Now that we have the time of flight, we can find the horizontal distance traveled by the bullet. Since the rifle was pointed directly at the center of the bull's-eye, the horizontal velocity (v) of the bullet remains constant throughout its flight.
Using the equation of motion for horizontal motion, we can find the horizontal distance (d) traveled by the bullet using the equation:
d = v * t (where v is the muzzle speed of the bullet and t is the time of flight)
Substituting the given values:
d = 795 m/s * 0.131 s
d ≈ 104.445 m
Therefore, the horizontal distance between the end of the rifle and the bull's-eye is approximately 104.445 meters.