Solve the Problem $\mathrm { R }$ Of a Projectile Is Related to the Initial Velocity

Multiple Choice

Solve the problem.
-The range $\mathrm { R }$ of a projectile is related to the initial velocity $\mathrm { v }$ and projection angle $\theta$ by the equation $R = \frac { v ^ { 2 } \sin 2 \theta } { g }$ , where $g$ is a constant. How is $d R / d t$ related to $d v / d t$ if $\theta$ is constant?

A) $\frac { \mathrm { dR } } { \mathrm { dt } } = \frac { 2 \mathrm { v } ^ { 2 } \cos 2 \theta } { \mathrm { g } } \frac { \mathrm { dv } } { \mathrm { dt } }$
B) $\frac { \mathrm { dR } } { \mathrm { dt } } = \frac { 2 \mathrm { v } \sin 2 \theta } { \mathrm { g } } \frac { \mathrm { dv } } { \mathrm { dt } }$
C) $\frac { d R } { d t } = \frac { 2 v } { g } \frac { d v } { d t }$
D) $\frac { \mathrm { dR } } { \mathrm { dt } } = \frac { 2 \mathrm { v } \cos 2 \theta } { \mathrm { g } } \frac { \mathrm { dv } } { \mathrm { dt } }$