question_answer

If a projectile has a 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.

Answer:

                Horizontal range, \[R=\frac{{{u}^{2}}\sin 2\theta }{g}\] Differentiating it w.r.t g, we have          \[\frac{dR}{dg}=-\frac{{{u}^{2}}}{{{g}^{2}}}\sin 2\theta \][\[\because \,\]u and \[\theta \] are constant] or\[dR=-\frac{{{u}^{2}}\sin 2\theta }{g}\frac{dg}{g}=-R\frac{dg}{g}\]or\[\frac{dR}{R}=-\frac{dg}{g}\]