What Formula Should I Use to Solve a Horizontal Projectile Problem?

[xelda]

A hunter aims directly at a small target (on the same level) 68 m away. If the bullet leaves the gun at a speed of 186 m/s, by how much will it miss the target?

I just need to know what formula I should use to solve this problem?

 

[Galileo]

First calculate the time it takes for the bullet to traverse the given distance.
Then calculate the amount by which the bullet dropped due to gravity.

 

[xelda]

I understand that's how to solve the problem, but I still don't think I'm doing this correctly. To calculate the time, I took 186 m/s divided by 68 m and got 2.735 s. Then I plugged the time into the equation y=yo+vyot-1/2gt^2. So it looked like 0+186m/s(2.735s)-1/2(9.8m/s^2)(2.735s)^2. I ended up with 472 but this number seems too large? Am I doing something wrong here?

Thank you for the quick response. I appreciate your help.

 

[Galileo]

You seem to have confused a few things.
You have to treat the horizontal and vertical components independently.
First, since there is no horizontal acceleration, the horizontal velocity is constant.
To get the time traveled, use d=vt. (d=distance, v=velocity, t=time) (so t=d/v)

Then for the vertical component, you can use $y(t)=y_0+vt-1/2gt^2$, but
think about what v is in this equation. It's the initial component of the velocity in the y-direction.

 

[xelda]

Okay, I used 9.9 m/s^2 for v and my final answer came to 2.93 m. Does this seem more accurate? I guess I was way off. :x

 

[Galileo]

What value did you find for t? And what is the initial v in the vertical direction?

 

[xelda]

For t I got .3656 s. I put 0 in for yo but should v also be 0 if it's the vertical component?

 

[Galileo]

For t I got .3656 s. I put 0 in for yo but should v also be 0 if it's the vertical component?

If the target is on the same level as the gun, then isn't the initial velocity horizontal?

 

[xelda]

Oh, okay. Now it's starting to make more sense. Since the initial velocity is horizontal, then it would be 0.