Finding the Distance to the Target from a Hunter's Rifle

How can we calculate the distance to the target from a hunter's rifle?

A hunter aims horizontally at a target on the same level as his rifle. If the bullet leaves his rifle at a velocity of 154.6 m/s and hits 0.64 meters below the target, how far away is the target?

Answer:

The distance to the target from a hunter's rifle can be calculated by determining the horizontal position of the bullet at the time it hits the target.

When the bullet leaves the rifle, it follows a parabolic trajectory due to the effects of gravity. We can use the given information about the initial velocity of the bullet, the acceleration due to gravity, and the vertical position of the bullet to solve for the time it takes for the bullet to hit the target.

By setting up the kinematic equations for motion in the x and y directions, we can find the time it takes for the bullet to reach the target. Substituting the values provided, we calculate that it takes 0.36 seconds for the bullet to hit the target.

Using the time calculated, we can then determine the horizontal position of the bullet at that time to find the distance to the target. Multiplying the initial velocity of the bullet by the time taken gives us a distance of 55.87 meters to the target.

Therefore, the target is approximately 55.87 meters away from the hunter's rifle when the bullet hits the target.