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Solve the Problem RR Of a Projectile Is Related to the Initial Velocity

Question 494

Multiple Choice

Solve the problem.
-The range RR of a projectile is related to the initial velocity vv and projection angle θ\theta by the equation R=v2sin2θg\mathrm { R } = \frac { \mathrm { v } ^ { 2 } \sin 2 \theta } { \mathrm { g } } , where g\mathrm { g } is a constant. How is dR/d\mathrm { dR } / \mathrm { d } t related to dv/dt\mathrm { dv } / \mathrm { dt } and dθ/dt\mathrm { d } \theta / \mathrm { dt } if neither vv nor θ\theta is constant?


A) dRdt=vg(vcos2θdθdt+2sin2θdvdt) \frac { d R } { d t } = \frac { v } { g } \left( v \cos 2 \theta \frac { d \theta } { d t } + 2 \sin 2 \theta \frac { d v } { d t } \right)
B) dRdt=1g(vcos2θdvdt+sin2θdθdt) \frac { d R } { d t } = \frac { 1 } { g } \left( v \cos 2 \theta \frac { d v } { d t } + \sin 2 \theta \frac { d \theta } { d t } \right)
C) dRdt=2vg(vcos2θdθdt+sin2θdvdt) \frac { d R } { d t } = \frac { 2 v } { g } \left( v \cos 2 \theta \frac { d \theta } { d t } + \sin 2 \theta \frac { d v } { d t } \right)
D) dRdt=1 g(4vcos2θdθdtdvdt) \frac { \mathrm { dR } } { \mathrm { dt } } = \frac { 1 } { \mathrm {~g} } \left( 4 \mathrm { v } \cos 2 \theta \frac { \mathrm { d } \theta } { \mathrm { dt } } \frac { \mathrm { dv } } { \mathrm { dt } } \right)

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