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If a projectile has constant initial speed and angle of projection, find the relation between the changes in the horizontal range due to change in

acceleration due to gravity.



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X = u cos Ф t
y = u sin Ф t - 1/2 g t²

velocity in vertical direction = dy/dt = u sin Ф - g t
       it becomes 0,  when  t = u sinФ / g.
       At this point of time the project reaches the highest altitude.

In this duration horizontal distance travelled is = x = u CosФ t * u sin Ф / g
           Range is twice this distance

  so R =  u² Sin2Ф / g

So horizontal range is inversely proportional to the acceleration due to gravity.
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