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

question 119

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) \(d s = \frac { 2 v \sin ( 2 \alpha ) } { g } d v - \frac { 2 v ^ { 2 } \cos ( 2 \alpha ) } { g } d \alpha\)

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