Physics Force & Motion ETEA 2022
PMDC Verified Question 74 of 137
A projectile is thrown at an angle of \( 45^\circ \) with horizontal and its range is \( R_1 \). Another projectile is thrown at an angle of \( 45^\circ \) with vertical and its range is \( R_2 \). The relation between \( R_1 \) and \( R_2 \) is:
A
\( R_2 = 2R_1 \)
B
\( R_1 = 2R_2 \)
C
\( R_1 = R_2 \)
D
\( 3R_1 = R_2 \)
Tap any option to test your recall and reveal the step-by-step Propolis autopsy.

Propolis Cognitive Error Autopsy

Official Correct Choice:
Option C: \( R_1 = R_2 \)
Concept:

Standard kinematics uses the angle relative to the horizontal to calculate range.

Solution:

  • Projectile 1: Angle with horizontal is \( \theta_1 = 45^\circ \).


  • Projectile 2: Angle with the vertical is \( 45^\circ \). Because the axes are orthogonal (\( 90^\circ \)), the angle with the horizontal is \( 90^\circ - 45^\circ = 45^\circ \). So, \( \theta_2 = 45^\circ \).


  • Since both projectiles are effectively launched at the exact same horizontal angle (\( 45^\circ \)), assuming equal initial velocities, their ranges will be absolutely identical.


  • Therefore, \( R_1 = R_2 \).


Why other options are incorrect:

Any factor scaling implies the angles resulted in different trigonometric outputs, which is false here.

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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