Suppose you throw a ball off the edge of a cliff of height h.

>>8912006
45°

Post homework questions on the homework board.
>>>/hm/

Depends on air resistance. If negligible, which it's not, it'd be 45 degrees.

>>8912012
school's over, boyo

>>8912010
>>8912015
alright.

I was hoping for proofs but okay.

>>8912035
Setup the equation to get height as a function of theta (hint, mgsin(theta)), then take the derivative of both sides, set it equal to zero, solve for theta.

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>>8912037
Thanks

>>8912006
the fact that you are at a height h doesn't matter.

The angle is the same on flat ground at h=0, it's 45 degrees.

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>>8912010
>>8912015
>>8912077
got it

>>8912107
Isn't this only for flat ground? If you're elevated there's going to be some extra distance. The answer is definitely below 45°. It depends on the height difference.

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>>8912171
Yes it is. But if it achieves max distance on level ground, wouldn't it keep achieving this superiority over the other angles if there were a greater fall since horizontal velocity remains constant?

Also, a greater angle affords more time since sin(theta) would be higher = more time spent vertically as well.

I just wish I could prove it.

>>8912171
Try this simulator: http://www.walter-fendt.de/html5/phen/projectile_en.htm

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>>8912180
>>8912191
Oh, this simulator actually shows that 45 degrees isn't the optimal angle when there's an initial height greater than zero...

>>8912171
Turns out you're right, and the people saying it's 45 degrees are wrong. Using the simulator from >>8912191 given an initial height of 100m, mass 1kg, and gravitational acceleration of 9.81 the optimal angle is given as 17-18 degrees as predicted in my original answer from >>8912070

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>>8912219
plugged 45 degrees as the angle; turns out a height of 0 is needed for 45 degrees to be the optimal angle for max range.

>>8912010
>>8912015
>>8912077

>>8912180
Imagine these arcs continuing if you moved the ground down 20 feet. Which one would move the farthest horizontally?

>>8912368

I'd imagine the 30 degree one, since it has a greater x component of velocity.

Depends on whether the 30 degree ball could catch up to the 45 degree one given the time.

>>8912191
>http://www.walter-fendt.de/html5/phen/projectile_en.htm
i fucking hate when "educational" "simulators" put arbitrary limits on value range

>>8912368
I think the greater the height the lower the angle. If the initial height is really high, close to infinity, then the ball traveling close to 0 degrees in a straight line horizontally would give it the max distance.

>>8912006
You're asking the wrong question if you want to find out how to throw the ball so that it travels the it's maximum horizontal distance. You should be asking how high up you need to go and how fast you need to throw the ball so that it enters a stable orbit and thus travels an infinite horizontal distance.

Infinity is the maximum.

Pi/4 radians

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It depends on initial height. If you use g = 9.81 m/s^2 and [math]V_0[/math] = 10 m/s you can see some horizontal distance vs launch angle (in rad) plotted here, with 3 sample initial heights. Each maximum occurs at a different angle. If you're curious, the equation for horizontal distance ends up being this (with x and h in meters and [math]V_0[/math] in m/s): [eqn]x(\theta,h,V_0,g)=V_0cos(\theta) (\frac{V_0 sin(\theta)}{g} +
\sqrt{\frac{2gh + {V_0}^{2} sin(\theta)^2}{g^{2}}})[/eqn]

>>8912780
Neat. What did you use to make the graph?

>>8912780
Forgot to add that the optimal angle is [math]\theta = {cos^{-1}}(\frac{\sqrt{2gh+{V_0}^2}}{\sqrt{2gh+2{V_0}^2}})[/math]

>>8912801
Mathematica

>>8912810
Could you graph something that would have that optimal angle as well as the angle found in >>8912070 to see if they return the same results?

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>>8912833
They're equal

>>8912849
Ah, good. What program did you use? Is that matlab?

>>8912851
Mathematica. It's handy but it's pretty pricey.

>>8912859
Gonna have to see about getting it when i have $$$.

>>8912006
I'm pretty sure it's 45 degrees

Wtf I was taught wrong?

Niggers wtf, the 45 degree shit only works when you are on a flat ground. You all failed basic mechanics.