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

---

Definitions:

Binomial Probability

The probability of achieving a specific number of successes in a fixed number of Bernoulli trials with the same probability of success on each trial.

Normal Curve

A bell-shaped curve that is symmetrical about the mean, representing the distribution of a continuous random variable.

Continuity Correction

An adjustment made when using a continuous probability distribution to approximate a discrete distribution.

Binomial Random Variable

A type of discrete random variable that represents the number of successes in a fixed number of binary experiments.