Solving Horizontal Rifle Bullet Gravity Problem

[nasjo30]

Homework Statement

A horizontal rifle is fired at a bull's-eye. The muzzle speed of the bullet is 785 m/s. The barrel is pointed directly at the center of the bull's-eye, but the bullet strikes the target 0.029 m below the center. What is the horizontal distance between the end of the rifle and the bull's-eye?

Homework Equations

Kinematic Equations

The Attempt at a Solution

I tried creating a right triangle with the data but it didn't work and now I am frustrated.

 

[fiziksfun]

use the equation delta d = v(i)t + .5at^2

delta h (vertical) = .5at^2 where a is -9.81 m/s^2 [since v(i) in the vertical direction is 0)

-.029 = (.5)(-9.81)t^2

t=?

so you can solve for time and plug it into the equation again to get horizontal distance, right?

delta d (horizontal) = v(i)t [note, there is no acceleration in the horizontal direction)

where v(i) 785 m/s

 

[thomate1]

I understand your frustration when trying to solve a problem and not getting the desired result. However, I would suggest taking a step back and approaching the problem in a systematic manner. First, we need to identify the relevant equations that can help us solve this problem. In this case, the kinematic equations, which relate the initial velocity, final velocity, acceleration, and displacement, can be used to solve for the horizontal distance.

Let's start by writing down the given information. We know that the muzzle speed of the bullet (v0) is 785 m/s and the bullet strikes the target 0.029 m below the center (Δy = -0.029 m). We also know that the bullet is fired horizontally, so there is no initial vertical velocity (v0y = 0) and the acceleration due to gravity (g) is acting only in the vertical direction.

Now, we can use the kinematic equation for displacement in the y-direction (Δy = v0yt + 1/2at^2) to solve for the time (t) it takes for the bullet to reach the target. Plugging in the known values, we get -0.029 m = 0 + 1/2(-9.8 m/s^2)t^2. Solving for t, we get t = 0.024 seconds.

Next, we can use the kinematic equation for displacement in the x-direction (Δx = v0xt) to solve for the horizontal distance (Δx) between the rifle and the bull's-eye. Plugging in the known values, we get Δx = (785 m/s)(0.024 s) = 18.84 m.

Therefore, the horizontal distance between the end of the rifle and the bull's-eye is approximately 18.84 meters. I hope this approach helps you in solving the problem. Remember, taking a systematic and logical approach is key in solving scientific problems.