A Little Physics Help

[Dimitrius]

So I'm helping this friend of mine out on her physics class and I don't really remember how to do this. So I'm attaching a translated pic of the problem:




I need a step-by-step explanation.

[Ħ]

45 degrees.


inb4 Sigz and/or FW

[DebraKadabra]

Don't ask me - the one semester of Physics I took my senior year of high school I barely passed.

[SystematicThought]

This just reminded me of Physics last year and I want to die...

[rumborak]

Differentiate, set to zero, solve.

[Scorpion]

Differentiate, set to zero, solve.

This. Which would lead to

45 degrees.

I think.

[Chino]

I can't help with this for shit, but I am curious about something. There is no other information provided. Wouldn't things like the cannon ball size and weight factor into the range? Or is that covered in that formula I don't understand?

Also, couldn't this equation just be plugged into a graphing calculator and graphed? Just find the maximum height of the curve along y-axis and that should be your maximum range. No?

[Dimitrius]

I can't help with this for shit, but I am curious about something. There is no other information provided. Wouldn't things like the cannon ball size and weight factor into the range? Or is that covered in that formula I don't understand?

Not necessarily. You can answer with  theta = y sin x (to give an example) and it would be a correct answer.



Where I'm really having the problem is with the tan part of it, I haven't done a problem like this in 3+ years so I completely forgot all those sin, cos, tan rules.

[jasc15]

Differentiate, set to zero, solve.

This, but the function to use is not the one shown.  You need to get D in terms of theta (the angle).

I can't help with this for shit, but I am curious about something. There is no other information provided. Wouldn't things like the cannon ball size and weight factor into the range? Or is that covered in that formula I don't understand?

This branch of dynamics, kinematics, does not deal with mass and forces, only with displacements, velocities and accelerations.  Kinetics would start to deal with things like mass, energy and momentum.

Also, couldn't this equation just be plugged into a graphing calculator and graphed? Just find the maximum height of the curve along y-axis and that should be your maximum range. No?

Yes, but the analytic way to do what you've described is what rumborak said.

[Aefenwelg]

Range = V^2 * sin(2theta)/g

so, differentiating with respect to theta:
Range' = V^2 * cos(2theta)*2/g

set Range' = 0:
cos(2theta) = 0

2theta = 90 (degrees)
theta = 45 (degrees)

[Aefenwelg]

You can actually forget all of that.
The problem you have is slightly different than the problem I gave an answer for, which is an angled cannon on a flat surface, not a hill.

[Dimitrius]

I figured it out, thanks anyway.

But yes, if it was on a flat surface the answer will always be 45 degrees.

[jsem]

I figured it out, thanks anyway.

But yes, if it was on a flat surface the answer will always be 45 degrees.

In a perfect world with no air resistance that is.