Physics Force & Motion NUMS 2024
PMDC Verified Question 15 of 137
In projectile motion for which angle maximum height is half its range?
A
\( 73^\circ \)
B
\( 65^\circ \)
C
\( 63^\circ \)
D
\( 68^\circ \)
Tap any option to test your recall and reveal the step-by-step Propolis autopsy.

Propolis Cognitive Error Autopsy

Official Correct Choice:
Option C: \( 63^\circ \)
Concept:

Solve the geometric relation for Range and Maximum Height.

Formula:

$$ \frac{H}{R} = \frac{\tan\theta}{4} $$

Solution:

  • The prompt specifies that Height is half of Range: \( H = 0.5 R \).


  • Therefore, \( \frac{H}{R} = 0.5 \).


  • Substitute this in: $$ 0.5 = \frac{\tan\theta}{4} \implies \tan\theta = 2 $$


  • Take inverse tangent: \( \theta = \tan^{-1}(2) \approx 63.4^\circ \).


  • Rounding gives \( 63^\circ \).


Why other options are incorrect:

Using \( R=H/2 \) gives \( \tan\theta = 8 \) (approx \( 83^\circ \)). The other angles do not yield a tangent of 2.

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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