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Question #2904
A 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
2012-03-06T11:21:03-0500
A 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.

Let's denote the distance as S and write the equations of the motion under the gravitational acceleration:
H = h0 + Vy*t - gt2/2
S = Vx*t.
Here Vx = V0*cos(&alpha;), Vy = V0*sin(&alpha;), h0 = 0, H = 0.

0& =& Vo sin(&alpha;)t - gt&sup2;/2; &
t =0;& t = 2V0*sin(&alpha;)/g
S = V0*cos(&alpha;)t &
S& = 2V0*cos(&alpha;)V0*sin(&alpha;)/g = V0*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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