# Homework Help: Angle for greatest range

1. Feb 7, 2010

### larryboi7

How can i find the angle of which an object will be thrown the farthest?

I know the angle will be 45 degrees if it were to be catched at the same height it were thrown, but what I'm looking for is the angle if it were 3meters off the ground.

Thank you for the help.

Last edited: Feb 7, 2010
2. Feb 7, 2010

### Staff: Mentor

Welcome to the PF. Are you familiar with how to maximize a function using differentiation? Write an equation for the range as a function of launch angle (given your offset y information). Show us your attempt at a solution so we can help.

3. Feb 7, 2010

### larryboi7

The equation would be

initial velocity is 5m/s

0 = 3 + 5sin(x) - (1/2)gt^2

x(t) = 5cos(x) * t

I know what differentiation is but I cant see how it will work to find the angle for maximum range.

4. Feb 7, 2010

### Staff: Mentor

I'm not understanding what you wrote, but it sounds like you can figure this out. BTW, is it thrown at 0m and caught at 2m, or the other way around?

I think you will write two equations (this is the usual way to solve this type of question): One for the horizontal motion, which has a constant velocitty. The other is the vertical motion equation, which involves the vertical pull of gravity. You will use them as simultaneous equations, and solve them for the final simultaneous (x,y) point. Does that help? Show us your work....

5. Feb 7, 2010

### larryboi7

it is thrown at 3m and and caught at 0 meters.
i have the equations as stated before. would you mind showing me?