AP EAMCET · PHYSICS · Motion In Two Dimensions
If the equation of motion of a projectile is \(\mathrm{y}=\mathrm{Ax}-\mathrm{Bx}^2\), then the ratio of the maximum height reached and the range of the projectile is
- A \(\frac{\mathrm{A}}{4}\)
- B \(\frac{\mathrm{A}}{B}\)
- C \(\frac{\mathrm{B}}{4}\)
- D \(\frac{\mathrm{A}^2}{\mathrm{~B}}\)
Answer & Solution
Correct Answer
(A) \(\frac{\mathrm{A}}{4}\)
Step-by-step Solution
Detailed explanation
Range \(R\): \(y=0 \implies Ax - Bx^2 = 0 \implies x(A - Bx) = 0\) \(R = A/B\) Maximum Height \(H\): \(\frac{dy}{dx} = A - 2Bx = 0 \implies x_H = A/(2B)\) \(H = A(A/(2B)) - B(A/(2B))^2 = A^2/(2B) - A^2/(4B) = A^2/(4B)\) Ratio \(\frac{H}{R}\):…
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