क्षैतिज से \(15^{\circ}\) के कोण पर प्रक्षेपित किए गए प्रक्षेप्य परास \(50 \mathrm{~m}\) है। यदि प्रक्षेप्य को समान वेग से क्षैतिज से \(45^{\circ}\) के कोण पर प्रक्षेपित किया जाता है, तो इसका परास होगा\(........\,m\)

A \(50\)
B \(50 \sqrt{2}\)
C \(100\)
D \(100 \sqrt{2}\)

Verified Solution

Answer & Solution

Correct Answer

(C) \(100\)

Step-by-step Solution

Detailed explanation

\(R =\frac{ v ^2 \sin 2 \theta}{ g }\) \(R \propto \sin (2 \theta)\) \(\frac{ R _1}{ R _2}=\frac{\sin \left(2 \theta_1\right)}{\sin \left(2 \theta_2\right)}=\frac{\sin (2 \times 15)}{\sin (2 \times 45)}=\frac{\sin 30^{\circ}}{\sin 90^{\circ}}\) \(\frac{50}{ R _2}=\frac{1}{2}\)…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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