Physics Force & Motion NUMS 2024
PMDC Verified Question 16 of 137
The horizontal range of projectile will be maximum when?
A
\( \sin\theta \approx 1 \)
B
\( \sin(2\theta) \approx 1 \)
C
\( \sin\theta \approx 0 \)
D
\( \sin(2\theta) \approx 0 \)
Tap any option to test your recall and reveal the step-by-step Propolis autopsy.

Propolis Cognitive Error Autopsy

Official Correct Choice:
Option B: \( \sin(2\theta) \approx 1 \)
Concept:

Mathematical boundaries of the range equation.

Formula:

$$ R = \frac{v_i^2 \sin(2\theta)}{g} $$

Solution:

  • Range \( R \) is directly proportional to the term \( \sin(2\theta) \).


  • The mathematical sine function hits its absolute peak value at exactly 1.


  • Therefore, maximum range occurs exactly when the factor \( \sin(2\theta) = 1 \).


Why other options are incorrect:

Option A corresponds to max height. Options C and D result in zero trajectory.

Quality & Fidelity Assurance: Every question on BeambePrep is rigorously curated against the official PMDC syllabus with zero filler, zero out-of-syllabus content, and zero typos. When an authentic past paper originally contained a historical mistake or ambiguity from the examining board (such as UHS or NUMS), BeambePrep faithfully reflects the original paper while detailing the nuance and scientific consensus in the autopsy above.

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