Physics Force & Motion SZABMU 2022
PMDC Verified Question 65 of 137
The angle of a projection of a projectile for which its maximum height and horizontal range are equal is:
A
\( 86^\circ \)
B
\( 46^\circ \)
C
\( 66^\circ \)
D
\( 76^\circ \)
Tap any option to test your recall and reveal the step-by-step Propolis autopsy.

Propolis Cognitive Error Autopsy

Official Correct Choice:
Option D: \( 76^\circ \)
Concept:

There is a fundamental relation between the Height (H) and Range (R) of a projectile based solely on its launch angle.

Formula:

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

Solution:

  • The problem states that Range equals Height (\( R = H \)).


  • Substitute this into the equation: $$ \frac{H}{H} = \frac{\tan\theta}{4} $$


  • $$ 1 = \frac{\tan\theta}{4} \implies \tan\theta = 4 $$


  • Taking the inverse tangent: $$ \theta = \tan^{-1}(4) \approx 75.96^\circ $$


  • Rounding to the nearest whole degree gives \( 76^\circ \).


Why other options are incorrect:

At \( 45^\circ \), Range is 4 times the Height. 66° and 86° do not satisfy the \( \tan\theta = 4 \) condition.

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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