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A rifle shoots bullets at [tex]48 \, \text{m/s}[/tex] and is aimed at a target [tex]45.7 \, \text{m}[/tex] away. If the center of the target is level with the rifle, how high above the target must the rifle barrel be pointed so that the bullet hits dead center?

Answer :

Final answer:

To hit the target dead center, the rifle barrel must be pointed approximately 4.42 meters above the target.

Explanation:

To calculate how high above the target the rifle barrel must be pointed, we can use the kinematic equations of motion. The time it takes for the bullet to reach the target can be found using the equation: time = distance / velocity. In this case, the distance is 45.7m and the velocity is 48m/s, so the time is: time = 45.7m / 48m/s = 0.95s.

Next, we can calculate the height the bullet will drop during this time. The equation for the vertical displacement of a projectile under constant acceleration is: displacement = initial velocity * time + 0.5 * acceleration * time^2. Since the bullet is shot horizontally, its initial vertical velocity is 0. Therefore, the equation simplifies to: displacement = 0.5 * acceleration * time^2. Considering the acceleration due to gravity, which is approximately -9.8m/s^2, and plugging in the values, we get: displacement = 0.5 * -9.8m/s^2 * (0.95s)^2 = -4.42m.

Since we want the barrel of the rifle to be pointed above the target, the answer is the opposite of the displacement value: height above target = -(-4.42m) = 4.42m. Therefore, the rifle barrel must be pointed approximately 4.42 meters above the target to hit dead center.

Learn more about Projectile motion here:

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