If You Throw a Stone into the Air at an Angle

question 81

Multiple Choice

If you throw a stone into the air at an angle of $\theta$ to the horizontal, it moves along the curve $y=x \tan \theta-\frac{x^{2}}{100}\left(1+\tan ^{2} \theta\right)$ , where y is the height of the stone above the ground, x is the horizontal distance.If the angle $\theta$ is fixed, what value of x gives the maximum height? (Your answer will $\theta$ .)

• A) \(\frac{50 \tan \theta}{1+\tan ^{2} \theta}\)
• B) \(\frac{1+\tan ^{2} \theta}{50 \tan \theta}\)
• C) \(\frac{\tan \theta}{50+50 \tan ^{2} \theta}\)
• D) \(\frac{50+50 \tan ^{2} \theta}{\tan \theta}\)

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