સમાન શરૂઆતના વેગથી સમક્ષિતિજ સાથે \(42^{\circ}\) અને \(48^{\circ}\) ના ખૂણે બે પદાર્થોને પ્રક્ષિપ્ત કરતાં તેની અવધિ અને ઊંચાઈ અનુક્રમે \({R}_{1}, {R}_{2}\) અને \({H}_{1}\), \({H}_{2}\) છે. તેના માટે સાચો વિકલ્પ કયો છે.

A \({R}_{1}>{R}_{2}\) અને \({H}_{1}={H}_{2}\)
B \({R}_{1}={R}_{2}\) અને \({H}_{1}<{H}_{2}\)
C \({R}_{1}<{R}_{2}\) અને \({H}_{1}<{H}_{2}\)
D \({R}_{1}={R}_{2}\) અને \({H}_{1}={H}_{2}\)

Verified Solution

Answer & Solution

Correct Answer

(B) \({R}_{1}={R}_{2}\) અને \({H}_{1}<{H}_{2}\)

Step-by-step Solution

Detailed explanation

Range \({R}=\frac{{u}^{2} \sin 2 \theta}{{g}}\) and same for \(\theta\) and \(90-\theta\) So same for \(42^{\circ}\) and \(48^{\circ}\) Maximum height \({H}=\frac{{u}^{2} \sin ^{2} \theta}{2 {g}}\) \({H}\) is high for higher \(\theta\) So \({H}\) for \(48^{\circ}\) is higher…

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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