If a rifle is shot at a target that is 300 yards away. the bullet travels through the air at 2800 feet per second. how many feet above the target should the shooter aim to hit the bullseye?
300 yards = 900 ft
So, the bullet gets there in 0.32 seconds.
How far does the bullet fall in that time?
s = 1/2 at^2
To determine how many feet above the target the shooter should aim, we need to consider the bullet's trajectory and the time it takes to reach the target. Here's how you can calculate it:
Step 1: Convert the distance to yards into feet.
300 yards = 900 feet
Step 2: Calculate the time it takes for the bullet to reach the target.
Time = Distance / Velocity
Time = 900 feet / 2800 feet per second
Step 3: Calculate the vertical distance the bullet will drop during the travel time.
Vertical Distance = 0.5 * acceleration due to gravity * (Time)^2
Acceleration due to gravity is approximately 32.17 feet per second squared.
Step 4: Determine the aiming point above the target.
The bullet will drop during its flight, so the shooter needs to aim higher to compensate for this drop. The aiming point will be equal to the vertical distance calculated in step 3.
Let's perform the calculations:
Step 1: 300 yards = 900 feet
Step 2: Time = 900 feet / 2800 feet per second = 0.3214 seconds (rounded to 4 decimal places)
Step 3: Vertical Distance = 0.5 * 32.17 feet per second squared * (0.3214 seconds)^2 = 1.6467 feet (rounded to 4 decimal places)
Step 4: The shooter should aim approximately 1.6467 feet above the target to hit the bullseye.
Therefore, the shooter should aim around 1.6467 feet above the target to hit the bullseye.