A rifle is aimed horizontally at a target 46.0away. The bullet hits the target 2.30 below the aim point.
What is the bullet's flight time?
What is the velocity as it leaves the barrel?
Your numbers need dimensions. Are they in meters? Is the 2.30 in centimeters? Do you want the bullet speed in m/s?
For the flight time, figure out how long it takes a dropped object to fall 2.30 whatevers.
To find the bullet's flight time, we can use the equation for vertical motion:
h = vi*t + (1/2) * g * t^2
In this equation:
- h is the vertical displacement (2.30 m),
- vi is the initial vertical velocity (unknown),
- t is the flight time (unknown),
- g is the acceleration due to gravity (-9.8 m/s^2).
Since the rifle is aimed horizontally, the initial vertical velocity is zero (vi = 0), so the equation simplifies to:
h = (1/2) * g * t^2
Substituting the given values:
2.30 m = (1/2) * (-9.8 m/s^2) * t^2
Solving for t:
t^2 = (2 * 2.30 m) / (9.8 m/s^2)
t^2 = 0.469 s^2
t ≈ 0.685 s
Therefore, the bullet's flight time is approximately 0.685 seconds.
To find the velocity as the bullet leaves the barrel, we can use the equation for horizontal motion:
d = v * t
In this equation:
- d is the horizontal distance (46.0 m),
- v is the initial horizontal velocity (unknown),
- t is the flight time (0.685 s).
Rearranging the equation to solve for v:
v = d / t
Substituting the given values:
v = 46.0 m / 0.685 s
v ≈ 67.26 m/s
Therefore, the velocity as the bullet leaves the barrel is approximately 67.26 m/s.