Projectile motion rifle question

[i_linn]

Homework Statement

A rifle that shoots bullets at 442 m/s is to be aimed at a target 44.9 m away. If the center of the target is level with the rifle, how high (in cm) above the target must the rifle barrel be pointed so that the bullet hits dead center?

Homework Equations

y-y₀ = v₀sin(Ø₀)t-1/2gt²

The Attempt at a Solution

I am not really sure what to do to solve the equation I figured out that the time is .1 s but I believe that I need to find out what the angle Ø is to solve the equation and I don't know how to find it. I am not looking for the answer maybe just an idea on what direction to head.

 

[Xand888]

y-y0 = v0sin(Ø0)t-1/2gt2

"If the center of the target is level with the rifle"

This is the cue you need to interpret. Based on this cue you can *simplify* the above equation. This does assume that you know which way your angle is being measured. Think about the initial speed and the direction that the problem provides. Good Luck!

 

[i_linn]

What I am unsure about is do they want you to angle the rifle a certain amount of cm and have a parabolic type trajectory or actually raise it up and have the bullet fall to the target. And by simplify the equation I am guessing you mean that (y-y0) would be equal to 0 because it is landing at the same height that it left from but I am not sure

 

[Xand888]

I would have to say that you just need to find the distance the bullet falls before it hits the target, then, if one were to raise the level of the rifle by this distance, the next bullet would hit dead center. Since they want a distance in centimeters rather than an angle in radians or degrees, you don't need to worry about the angle --> This is a very nice simplification, as the problem states that the target and rifle are level - meaning your angle is 0. In real life you would probably tilt the rifle rather than find higher ground, but that approach should have been discarded when you're asked for a distance in centimeters (you would have to know the rifles length in order to project this tilt angle as a length). Hope that clears it up.

 

[i_linn]

OK so possibly it is the book that's wrong and not me because using that equation I got y=4.905cm but the answer online is

Number 5.056439020552 Units cm

I also used the books solution which is

and using my numbers I still get the 4.905 so I am pretty confused

 

[i_linn]

well nevermind I worked it out again and got the right answer still don't really understand the solution though

 

[DocZaius]

Since you got the right answer, I'll try to explain the problem.

Imagine that you are to shoot at a target but are not allowed to tilt the rifle in any way. The rifle must be kept parallel to the ground. But you are allow to raise the rifle as high as you want. You know that no matter how quickly the bullet travels horizontally, it will fall at a predictable acceleration vertically. That acceleration is g.

So first you find out how long it takes the bullet to horizontally get to the target's distance (for now ignore if you vertically hit the bull's eye or not). Then once you find that time, you find out the distance the bullet drops during that time. Once you know that distance, you raise the rifle by that distance and are sure to hit your target!