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# Answer to Question #1853 in Mechanics | Relativity for BALACHANDRA K

Question #1853
An projectile is fired uphill over ground with slope at an angle alpha to the horizontal.Find the direction in which it should be aimed to achieve the maximum range
1
2011-03-09T08:11:07-0500
Let's denote the distance as S and write the equations of the motion under the gravitational acceleration:
H = h0 + voyt - gt2/2
S = vox t
Where vox = Vo cos(&alpha;), voy = Vo sin(&alpha;), ho = 0, H = 0.

0 = Vo sin(&alpha;)t - gt2/2; t =0; t = 2Vo sin(&alpha;) / g
S = Vo cos(&alpha;)t
S = 2Vo cos(&alpha;)Vo sin(&alpha;) / g = Vo sin (2&alpha;) / g , the maximum value of sin(2&alpha;) is 1 at 2&alpha; = 90, hence
&alpha; = 45 degrees.

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