Physics Force & Motion ETEA 2023
PMDC Verified Question 38 of 137
When the range of a projectile is equal to one fourth of the height then which one is true:
A
\( \tan\theta = 10 \)
B
\( \tan\theta = 12 \)
C
\( \tan\theta = 16 \)
D
\( \tan\theta = 1 \)
Tap any option to test your recall and reveal the step-by-step Propolis autopsy.

Propolis Cognitive Error Autopsy

Official Correct Choice:
Option C: \( \tan\theta = 16 \)
Concept:

Utilize the standard identity linking Range, Height, and Launch Angle.

Formula:

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

Solution:

  • The problem states that Range is exactly one fourth of the Height: \( R = \frac{H}{4} \).


  • Rearranging gives: \( \frac{H}{R} = 4 \).


  • Substitute this into our identity: $$ 4 = \frac{\tan\theta}{4} $$


  • Multiply both sides by 4: $$ \tan\theta = 16 $$


Why other options are incorrect:

Misinterpreting the fraction (e.g., assuming \( H = R/4 \)) would yield \( \tan\theta = 1 \). Arithmetic errors lead to 10 or 12.

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.

Previous Question All Force & Motion MCQs Next Question

Want to solve full-length papers under timed exam conditions?

Practice with zero-scroll lockdown sprints, dynamic latency zone timers, live peer selection telemetry, and the automated Amber mistake recovery loop.

Enter Arena Sprint iOS App Android App