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Question #42075

Difficulty: 8/10 | 🟢 Free

The Question

A particle of mass $m$ is projected from the ground with an initial speed $u$ at an angle $\theta$ to the horizontal. It experiences a velocity-dependent drag force $\vec{F}_d = -m \beta \vec{v}$ , where $\beta$ is a positive constant and $\vec{v}$ is the instantaneous velocity. If the terminal velocity of the particle is $V_T$ and $u \ll V_T$ , which of the following expressions best approximates the horizontal range of the projectile? (Assume acceleration due to gravity is $g$ and neglect terms of order $(u/V_T)^2$ and higher).

Options

A.
$\frac{u^2 \sin 2\theta}{g} \left( 1 - \frac{4u \sin\theta}{3V_T} \right)$
B.
$\frac{u^2 \sin 2\theta}{g} \left( 1 - \frac{2u \sin\theta}{3V_T} \right)$
C.
$\frac{u^2 \sin 2\theta}{g} \left( 1 - \frac{4u \cos\theta}{3V_T} \right)$
D.
$\frac{u^2 \sin 2\theta}{g} \left( 1 - \frac{u \sin\theta}{V_T} \right)$

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Variable_Constraint

Develop pure symbolic logic skills by mastering algebraic constraints without relying on numerical data.

Concepts Behind This Question

Projectile Path Equation|Conservative vs Non-conservative|Approximations

Why This Question Is Tricky

Common Mistakes

This question tests the ability to handle non-conservative, velocity-dependent drag forces that break the symmetry of the standard parabolic trajectory.

Students often mistakenly assume that the time of flight remains unchanged or apply the drag correction only to the horizontal velocity.

The trap lies in failing to recognize that the vertical drag reduces the time of flight, which compounds with the horizontal deceleration.

Using the Taylor expansion to linearize the exponential decay of velocity is a crucial JEE Advanced approximation technique.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Motion in a Plane - Class 11 Part 1
Concept	Projectile Path Equation
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free