A hunter aims directly at a target (on the same level) 125m away. If the bullet leaves the gun at a speed of 227 m/s, by how much will it miss the target?

I'm not sure how to approach this problem. I know I need to find the horizontal distance traveled, probably by finding the time it takes for the bullet to fall to the earth.

However I do not know how to start this. Don't I need a height from which the bullet starts traveling?

I am assuming that you mean that the hunters gun and the center of the bullseye of the target are the same distance from the ground.

Considering the horizontal velocity of the bullet alone, it will reach the target in 125/227 = .55 sec.

In this .55 sec., gravity will pull the trajectory of the bullet down a distance of h = gt^2/2 = 9.8(.55)^2/2 = 1.48m, thereby missing the center of the bullseye by 1.48m. A realistic diameter of the bullseye would alter this result.

If the target were something like a ping-pong ball, the miss distance of 1.48m becomes more realistic.

To solve this problem, you don't need to know the height from which the bullet is fired. Since the problem mentions that the target and the hunter are on the same level, we can assume that the bullet is fired horizontally.

To find the horizontal distance traveled by the bullet, you can use the formula:

Horizontal distance = velocity × time

In this case, the horizontal distance traveled is equal to 125m because the target is 125m away. Now, let's find the time it takes for the bullet to reach the target.

Since the bullet is fired horizontally, its initial vertical velocity is zero. We can use the equation for vertical displacement to find the time of flight.

Vertical displacement = initial vertical velocity × time + (1/2) × acceleration due to gravity × time^2

Since the bullet is not influenced by a vertical force, the vertical displacement is zero. We can rearrange the equation to solve for time:

0 = (1/2) × (9.8 m/s^2) × time^2

Simplifying the equation:

0 = 4.9 × time^2

Dividing both sides by 4.9, we get:

0 = time^2

Since time cannot be negative, we know that time = 0.

Therefore, the time it takes for the bullet to reach the target is 0 seconds.

Now, using the formula:

Horizontal distance = velocity × time

Plugging in the given values:

Horizontal distance = (227 m/s) × (0 s)

The time is zero because the bullet hits the target instantaneously. Therefore, the horizontal distance traveled by the bullet is zero.

Thus, the bullet will not miss the target.