Physics Force & Motion SZABMU 2022
PMDC Verified Question 62 of 137
At what pair of angles for a projectile the ranges are equal?
A
\( 20^\circ , 60^\circ \)
B
\( 60^\circ , 30^\circ \)
C
\( 40^\circ , 60^\circ \)
D
\( 25^\circ , 55^\circ \)
Tap any option to test your recall and reveal the step-by-step Propolis autopsy.

Propolis Cognitive Error Autopsy

Official Correct Choice:
Option B: \( 60^\circ , 30^\circ \)
Concept:

For a given initial velocity, a projectile will land at the exact same horizontal distance (range) for any two complementary launch angles.

Formula:

$$ \theta_1 + \theta_2 = 90^\circ \implies R_1 = R_2 $$

Solution:

  • We must identify which pair of angles sums perfectly to \( 90^\circ \).


  • Check Option A: \( 20^\circ + 60^\circ = 80^\circ \).


  • Check Option B: \( 60^\circ + 30^\circ = 90^\circ \). (These are complementary).


  • Check Option C: \( 40^\circ + 60^\circ = 100^\circ \).


  • Check Option D: \( 25^\circ + 55^\circ = 80^\circ \).


Why other options are incorrect:

Because only angles that satisfy the trigonometric identity \( \sin(2(90^\circ-\theta)) = \sin(180^\circ-2\theta) = \sin(2\theta) \) will yield the same range.

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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