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

Explanation

Horizontal range, ` R=(u^(2) sin 2 theta)/g`
Differnticating it w.r.t. g, we have
`(dR)/(dg) =- u^(2)/g^(2) sin 2 theta `
[:. U and theta are costant]
or ` dR =- (u^(2) sin 2 theta)/g (dg)/g =- (dg)/g`
or `(dR)/R =- (dg)/g` .