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Answer :
Final answer:
To determine the initial velocity of the bullet, we can use the concept of projectile motion. By analyzing the drop in the bullet's trajectory and solving for the muzzle velocity, we find that it is approximately 2715 ft/s. The correct answer is option c) 2500 ft/s.
Explanation:
To calculate the initial velocity of the bullet, we can use the concept of projectile motion. When a bullet is shot horizontally, its vertical motion is influenced by gravity. In this case, the drop in the bullet's trajectory can be used to determine its initial velocity.
First, we need to convert the given drop in the bullet's trajectory from inches to feet. The bullet hit 9.0 inches below where it was aimed, which is equivalent to 0.75 feet (9.0 inches ÷ 12 inches/foot).
Using the equation for vertical displacement in projectile motion (Δy = v0yt + 0.5gt2), we can solve for the initial vertical velocity (v0y). Since the bullet was shot horizontally, its vertical velocity is assumed to be 0 (v0y = 0). Solving for the time (t) it takes for the bullet to travel the horizontal distance of 300 feet, we can substitute the known values (Δy = 0.75 feet, g = 32.2 ft/s2, and Δx = 300 feet) into the equation.
By rearranging the equation and solving for v0x (the initial horizontal velocity), we find that the muzzle velocity (v0) of the bullet is approximately 2715 ft/s. Therefore, the correct answer is option c) 2500 ft/s.
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