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

question 468

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) \(\frac { \mathrm { dR } } { \mathrm { dt } } = \frac { 2 \mathrm { v } \cos 2 \theta } { \mathrm { g } } \frac { \mathrm { dv } } { \mathrm { dt } }\)

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