Q.23 Physics ⭐ 360° Option Elimination Active

NEET 2023 Physics Question 23 Solution

Topic: Laws of Motion · Official NTA Booklet Code G5

Question

A football player is moving southward and suddenly turns eastward with the same speed to avoid an opponent. The force that acts on the player while turning is:

✓

Verified Against NTA Final Answer Key

Option (4) : along north-east

📚 Laws of Motion Easy

📋 Given Parameters & Problem Setup

Initial Velocity Direction Southward (-ĵ)

Final Velocity Direction Eastward (+î)

Speed Same speed v before and after turning

⚡

The 30-Second Exam Hall Shortcut: ⚡ Vector Subtraction Δv = v_f - v_i Shortcut

⏱️ Save ~35 seconds

Force is along change in velocity! Final is East (+î), Initial was South (-ĵ); Δv = East - (-South) = East + North = North-East in 5 seconds!

1 Force is parallel to change in momentum / velocity: F⃗ ∝ Δv⃗ = v⃗_f - v⃗_i.

2 Represent directions as unit vectors: East = +î, North = +ĵ, South = -ĵ.

3 Initial velocity v⃗_i = -v ĵ (Southward).

4 Final velocity v⃗_f = +v î (Eastward).

5 Change in velocity: Δv⃗ = v⃗_f - v⃗_i = v î - (-v ĵ) = v î + v ĵ.

6 +î (East) + +ĵ (North) points directly along North-East!

7 Immediately pick Option (4) along north-east!

🛡️

Why You Can 100% Trust This Shortcut: Fundamental Newtonian Mechanics · Impulse-Momentum Theorem (Force direction: F⃗ = dp⃗/dt ∝ Δv⃗ = v⃗_f - v⃗_i).

📐

Step-by-Step Rigorous Workflow & Mathematical Proof

Step 1

Relation Between Applied Force and Velocity Change

By Newton's second law of motion, the net external force F⃗ acting on the player is directly proportional to the rate of change of linear momentum, and therefore points in the direction of the change in velocity vector Δv⃗:

\vec{F} = m \frac{d\vec{v}}{dt} \approx m \frac{\Delta \vec{v}}{\Delta t} \implies \vec{F} \parallel \Delta \vec{v}

Step 2

Cartesian Coordinate Direction Representation

Let the positive x-axis represent East (+î), positive y-axis represent North (+ĵ), and negative y-axis represent South (-ĵ). With initial speed v:

\vec{v}_i = -v \hat{j} \quad (\text{Southward}), \qquad \vec{v}_f = v \hat{i} \quad (\text{Eastward})

Step 3

Calculation of Change in Velocity Vector

Subtract the initial velocity vector from the final velocity vector:

\Delta \vec{v} = \vec{v}_f - \vec{v}_i = v \hat{i} - (-v \hat{j}) = v \hat{i} + v \hat{j}

Step 4

Directional Orientation Determination

The vector v î + v ĵ has equal positive components along East and North, forming an angle of 45° between East and North:

\tan\theta = \frac{v_y}{v_x} = \frac{v}{v} = 1 \implies \theta = 45^\circ \quad (\text{North of East, i.e., North-East})

⭐

360° Option Elimination Engine Key Feature

Diagnose every choice: Know exactly why the right option works and why distractors fail.

4-Option Deep Scan

1 (1)

✗ Incorrect

Verdict & Scientific Reason:

Points diametrically opposite to the actual force vector.

⚠️

Student Fallacy (Why candidates pick this trap): Candidate subtracted v_f from v_i (calculated -v_f + v_i = -v î - v ĵ = South-West).

2 (2)

✗ Incorrect

Verdict & Scientific Reason:

Considers only the final velocity direction, ignoring the southward momentum that had to be arrested.

⚠️

Student Fallacy (Why candidates pick this trap): Candidate thought the force acts purely in the direction the player ultimately moves.

3 (3)

✗ Incorrect

Verdict & Scientific Reason:

Considers only the stopping force for southward motion, ignoring the eastward acceleration.

⚠️

Student Fallacy (Why candidates pick this trap): Candidate considered only the stopping force for southward motion.

4 (4)

✓ 100% Correct

Verdict & Scientific Reason:

Accurate direction: vector subtraction yields v î + v ĵ (North-East).

💡

Why this is airtight: None. Candidate correctly applied vector subtraction Δv = v_f - v_i.

⚠️

NTA Trap Alert: Confusing Direction of Motion with Direction of Force (Picking Eastward)

Many candidates intuitively answer "Eastward" because the player turned East. To turn East from South, the ground must push North (to cancel southward motion) AND East (to generate eastward motion), giving North-East.

🛡️ How to avoid the -1 mark: Force is along CHANGE in velocity: Δv = Final - Initial.

📖

Core NEET Syllabus Standard

National Eligibility cum Entrance Test (NEET UG) · Laws of Motion Standard Benchmark

Core Scientific Principle Tested:

"Net force is always oriented parallel to the change in momentum vector: F⃗ ∝ (v⃗_f - v⃗_i)."

Syllabus Focus: Newton's Second Law, Momentum, and Impulse Vectors

Preserved in Rationalized Curriculum Syllabus & Academic Standards ↗

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NEET 2023 Physics Question 23 Solution

Question

The 30-Second Exam Hall Shortcut: ⚡ Vector Subtraction Δv = v_f - v_i Shortcut

Step-by-Step Rigorous Workflow & Mathematical Proof

Relation Between Applied Force and Velocity Change

Cartesian Coordinate Direction Representation

Calculation of Change in Velocity Vector

Directional Orientation Determination

360° Option Elimination Engine Key Feature

NTA Trap Alert: Confusing Direction of Motion with Direction of Force (Picking Eastward)

Core NEET Syllabus Standard

Ready to attempt under real exam pressure?

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