A Ball Thrown from Ground Level with Initial Speed V $\alpha$

Multiple Choice

A ball thrown from ground level with initial speed v and at an angle $\alpha$ with the horizontal hits the ground at a distance $s = \frac { v ^ { 2 } \sin ( 2 \alpha ) } { g }$ away from the starting point (where g is the acceleration due to gravity) .Calculate the differential ds.

A) $d s = \frac { 2 v \sin ( 2 \alpha ) } { g } d v + \frac { 2 v ^ { 2 } \cos ( 2 \alpha ) } { g } d \alpha$
B) $d s = 2 v \sin ( 2 \alpha ) d v + 2 v ^ { 2 } \cos ( 2 \alpha ) d \alpha$
C) $d s = \frac { 2 v \sin ( 2 \alpha ) } { g } d v + \frac { 2 v ^ { 2 } \sin ( 2 \alpha ) \cos ( 2 \alpha ) } { g } d \alpha$
D) $d s = \frac { 2 v \sin ( 2 \alpha ) } { g } d v - \frac { 2 v ^ { 2 } \cos ( 2 \alpha ) } { g } d \alpha$