how to explain a theorietical calculation of best angle

[DannyN]

Hi guys, i've just finished doing a prac regarding motion. We got to play with a toy gun and investigate a few things. One of them was firing the bullet at different angles from 0-90 degrees and finding the horizontal distance. What i found was at 45 degrees, it covered the longest horizontal distance. How do i "show and explain a theoretical calculation of best angle?" Thanks in advance =D

[appianway]

Differentiate and find a maximum?

[schnappy]

A more year 12 physics friendly approach would be to make a spreadsheet, with a column for the range of the motion, and a column of angles from 0-90deg with many intervals. But the calculus approach would be just as easy if you know how to do it.

Rather than set dR/d(theta) = 0 (Using the range equation in terms of 2*theta which hopefully you know about), you can set the sine function to its maximum possible value. Which is 1, and you solve the trig equation. Avoids calculus in case your teacher doesn't like that, which my physics 3/4 teacher didn't.

[DannyN]

are we suppose to have learnt this O.o, i know how to differentiate problems but how i start off with an equation? do i need spring constants or something?

idk this is what i did, it's probably wrong LOL =P

R=sin2(theta)---->dR/d(theta)=2cos2(theta)

2cos2(theta)=0---->theta=pi/4

was my working just random luck? please explain more, oh btw i made a spreadsheet but the question asks me another way of proving the best angle

[/0]

Your working is correct. The equation has multiple solutions so you might want to explain why is the only reasonable angle in this case.
But as schnappy said, Calculus isn't expected in physics, so perhaps you should just note that and leave it there.

[schnappy]

My physics teacher didn't even like seeing radians anywhere. Not because he doesn't know much about them, he's a genius as most physics teachers are, but he's quite exam-centric. he use to joke and write 'bad' answers on the board regarding rounding... the answer is 3.65 newtons, not '3.64935342ei(pi) etc.'

No, you're not meant to have explicitely learnt this. Your working with the calculus method is correct. The full equation is R=vvsin2(theta)/g, and since vv/g is a constant you can bin it, and then you proceed. As you did

What exactly would you like to be explained more? Have you done applications of differentiation in methods? (If you don't do methods/specialist at all it might be best to avoid the calculus altogether in case your teacher likes to ping questions on you?)

[Asx4Life]

let theta=#
sin(2#) must equal maximum value of sine to give greatest Range.
hence sin(2#) must equal 1.
since sin(90)=1
2# must equal 90
then #=45

Hope it helped.