A rifle is fired horizontally and travels 200.0 m The rifle barrel is 1.90m from the ground. What speed must the bullet have been traveling at? Ignore friction.
How do I solve this ?
321m/s
320
To solve this problem, you can use the principles of projectile motion. Here are the steps to find the initial speed of the bullet:
Step 1: Identify the known quantities:
- Horizontal distance traveled by the bullet (range): 200.0 m
- Height of the rifle barrel from the ground: 1.90 m
- Acceleration due to gravity: 9.8 m/s^2 (assuming no air resistance)
Step 2: Determine the time it takes for the bullet to reach the target horizontally:
Since the bullet is fired horizontally, the vertical displacement is only due to gravity. We can use the formula for displacement to find the time it takes for the bullet to reach the target:
Vertical displacement (Δy) = 1/2 * g * t^2 [where g is the acceleration due to gravity and t is the time]
In this case, Δy = 1.90 m. Rearrange the formula to solve for time (t).
Step 3: Calculate the initial vertical velocity of the bullet:
The initial vertical velocity (v_y) is given by: v_y = g * t
Step 4: Calculate the initial horizontal velocity of the bullet:
The horizontal velocity (v_x) remains constant throughout the motion. Since there is no vertical acceleration horizontally, the horizontal distance traveled is equal to the horizontal velocity multiplied by the time:
Horizontal distance traveled = v_x * t
In this case, the horizontal distance is 200.0 m. Rearrange the formula to solve for v_x.
Step 5: Calculate the initial speed of the bullet:
The initial speed of the bullet (v) is the combined vector sum of the horizontal and vertical velocities:
v = √(v_x^2 + v_y^2)
By following these steps and evaluating the equations, you can calculate the required speed of the bullet.