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
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Expert's answer
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(α), voy = Vo sin(α), ho = 0, H = 0.
0 = Vo sin(α)t - gt2/2; t =0; t = 2Vo sin(α) / g S = Vo cos(α)t S = 2Vo cos(α)Vo sin(α) / g = Vo sin (2α) / g , the maximum value of sin(2α) is 1 at 2α = 90, hence α = 45 degrees.
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