# Maximum range of a rifle

1. Aug 16, 2008

### Lindeza

1. The problem statement, all variables and given/known data
A sport rifle used for target shooting has a muzzle velocity of 1200 ft/s
a) what is the maximum range of the rifle if it is fired about 5 feet above the ground?
b) how long would a bullet be in the air if it was fired for the maximum range?

2. Relevant equations

3. The attempt at a solution
I came up with 2 parametric equations. I don't know if they will help me though...
x= t*l1200lcos(0)
y= tl1200lsin(o)-16t²+5
I could maybe do this, if someone explained the topic to me. I don't understand parametric equations at all, unfortunately...

2. Aug 16, 2008

### HallsofIvy

Staff Emeritus
Am I the only one who thinks it peculiar that we have three consecutive problems that involve exactly the same equations?

Yes, those are the equations you need. Now apply those equations to these problems:

a) "what is the maximum range of the rifle if it is fired about 5 feet above the ground?"
The bullet is 5 feet above the ground when t= 0. What is its height when the bullet reaches the "maximum range of the rifle"?

b) "how long would a bullet be in the air if it was fired for the maximum range?"
Solve either of the equations you have "at maximum range" for t.

3. Aug 16, 2008

### tiny-tim

… troubles come in threes …

Hi HallsofIvy!
Yes … it's just you!

4. Aug 18, 2008

### Lindeza

so...you are saying:
a) t=0 in the equations and the solution is the answer???
b)for the maximum range i take the first derivative and solve it for t??

and yes, I know that it's sort of silly to post 3 problems involving the same equations...
I just really, really, really don't understand what I am supposed to do.
And since I am taking precal in summer school and over the internet, I don't have a teacher that I can ask these questions...
So you are my only help :)

5. Aug 18, 2008

### Topher925

a) Not quite. What your after is what is the value of Y when the bullet hits the ground.

b) Yes, take the derivative of Y and set it equal to 0, then solve for t. Do you know why you are doing this? After that, X should be easy. But be careful on how you define your coordinate system!

So does that mean we should be getting paid too?

6. Aug 18, 2008

### Lindeza

which variable do I have to set equal to zero to get the value of y when it hits the ground?
b) i actually think I understand what I am doing in b. I don't understand a at all though...
Thanks a lot for your help!

7. Aug 22, 2008

### HallsofIvy

Staff Emeritus
What does y MEAN here? What does it measure?