Help Maximizing Range of Projectile Motion

[Rowah]

My teacher gave me a project that requires us to find the angle that "produces the maximum range for a trebuchet with a release speed of 50 m/s."

My (Delta)h value is +46 and I have to calculate the range produced by 5 different angles, graph it, and find the best angle to a hundredth of a degree. I'm going to calculate for the angles 5, 25, 45, 65 and 85.

My Questions:

1) Are there any formulae or techniques that would allow me to figure out the best angle in advance? I know my teacher is a perfectionist and DEMANDS absolute accuracy! Would this formula work? I used it and got a value of 51.3542 degrees. http://scitation.aip.org/servlet/GetImg?key=PHTEAH000043000002000098000001%3A0%3A2%3A28&t=a&d=a

2) My (delta)h value is +46, my teacher said "it would apply to a group trying to target a castle 50 meters above them." Does that mean (delta)y is equal to +46?

Thanks in Advance ^_^

 

[FunkyDwarf]

ok logically you can deduce the answer but its better to work it out this way a.) because youll understand it better and b.) because youll get marks for working

you know Newtons laws of motion
ok logically you can deduce the answer but its better to work it out this way a.) because youll understand it better and b.) because youll get marks for working

Newtons laws of motion tell you:
$$s = ut + (1/2)a{t^2}$$

You can, from your information, work out the component (verticle and horizontal) form of your velocity. From the above equations you work out when the projectile will hit the ground solving for time (be careful, this produces a quadratic, think what the other solution might be!) when you have this time constant you multiply by your horizontal component to get max distance.

hope this helps
-G

 

[Rowah]

Sorry, I'm only in Grade 12 physics, I don't understand >_<

I have no idea what "s" and "u" are.

 

[radou]

...Newtons laws of motion tell you:
$$s = ut + (1/2)a{t^2}$$...

This equation doesn't have anything to do with Newtons law of motion, which are a part of dynamics, and not kinematics.

's' represents displacement, and 'u' represents velocity.

 

[FunkyDwarf]

ok fair point, its not from Newtons laws but he derived them when he basicallyt made up calculus (which made the universe more complicated and school harder :) )

but at the year 12 level those equations should be common place

 

[Rowah]

Cool, I finished the assignment, thanks guys :D