Q.177 Physics ⭐ 360° Option Elimination Active

NEET 2020 Physics Question 177 Solution

Topic: Motion in a Straight Line · Official NTA Booklet Code E1

Question

A ball is thrown vertically downward with a velocity of 20 m/s from the top of a tower. It hits the ground after some time with a velocity of 80 m/s. The height of the tower is: (g = 10 m/s²)

✓

Verified Against NTA Final Answer Key

Option (4) : 300 m

📚 Motion in a Straight Line Easy

📋 Given Parameters & Problem Setup

Initial Downward Speed (u) 20 m/s

Final Speed on Ground (v) 80 m/s

Acceleration due to Gravity (g) 10 m/s^2

⚡

The 30-Second Exam Hall Shortcut: ⚡ "v^2 = u^2 + 2 g h => h = (v^2 - u^2) / (2g) = (80^2 - 20^2) / 20 = (6400 - 400) / 20 = 6000 / 20 = 300 m!"

⏱️ 20 seconds

Using the third kinematic relation v^2 = u^2 + 2gh: h = (v^2 - u^2) / (2g) = (80^2 - 20^2) / (2 × 10) = (6400 - 400) / 20 = 6000 / 20 = 300 m. Instant 5-second calculation for Option (4)!

1 Formula:

v^2 = u^2 + 2 g h

2 Rearrange for height:

h = \frac{v^2 - u^2}{2g}

3 Substitute:

v = 80\text{ m/s}

u = 20\text{ m/s}

g = 10\text{ m/s}^2

4 Compute:

h = \frac{6400 - 400}{20} = \frac{6000}{20} = 300\text{ m}

5 Select Option (4).

🛡️

Why You Can 100% Trust This Shortcut: NCERT Physics · Motion in a Straight Line (Kinematic Equations for Uniform Acceleration)

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Step-by-Step Rigorous Workflow & Mathematical Proof

Step 1

Identify Kinematic Parameters

Choose downward direction as positive: - Initial velocity: $u = +20\text{ m/s}$ - Final velocity upon hitting ground: $v = +80\text{ m/s}$ - Acceleration: $a = +g = +10\text{ m/s}^2$ - Displacement: $s = h$ (height of the tower).

Step 2

Select Third Equation of Motion

Because time $t$ is not specified, use the work-energy / kinematic relation independent of time: $v^2 = u^2 + 2 g h$ .

Step 3

Solve for Height h

$h = \frac{v^2 - u^2}{2g} = \frac{(80)^2 - (20)^2}{2 \times 10} = \frac{6400 - 400}{20} = \frac{6000}{20} = 300\text{ m}$ .

Step 4

Conclude and Verify

Matches Option 4.

⭐

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 A

✗ Incorrect

Verdict & Scientific Reason:

Incorrect; arithmetic sign and calculation error.

⚠️

Student Fallacy (Why candidates pick this trap): Using (6400 + 400)/20 and miscalculating.

2 B

✗ Incorrect

Verdict & Scientific Reason:

Incorrect; mistakenly adds initial kinetic energy (v^2 + u^2)/20 = (6400 + 400)/20 = 340 m.

⚠️

Student Fallacy (Why candidates pick this trap): Adding instead of subtracting u^2.

3 C

✗ Incorrect

Verdict & Scientific Reason:

Incorrect; assumes the ball was dropped from rest (u = 0): 80^2 / 20 = 320 m.

⚠️

Student Fallacy (Why candidates pick this trap): Ignoring the initial downward speed of 20 m/s.

4 D

✓ 100% Correct

Verdict & Scientific Reason:

Accurate value; h = (80^2 - 20^2)/20 = 6000 / 20 = 300 m.

💡

Why this is airtight: None; correct application of v^2 = u^2 + 2gh.

⚠️

NTA Trap Alert: Dropped vs Thrown Downward

Students often assume u = 0, giving h = 80^2 / 20 = 320 m (Option C). The question clearly states it was THROWN downward with 20 m/s!

🛡️ How to avoid the -1 mark: Look for initial velocity keywords: 'dropped' means u = 0; 'thrown' means u != 0.

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Core NEET Syllabus Standard

Physics · Motion in a Straight Line Standard Benchmark

Core Scientific Principle Tested:

Syllabus Focus: Height of a Tower from Initial Downward Velocity and Impact Speed

✓ Core NEET UG Syllabus Anchor Syllabus & Academic Standards ↗

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NEET 2020 Physics Question 177 Solution

Question

The 30-Second Exam Hall Shortcut: ⚡ "v^2 = u^2 + 2 g h => h = (v^2 - u^2) / (2g) = (80^2 - 20^2) / 20 = (6400 - 400) / 20 = 6000 / 20 = 300 m!"

Step-by-Step Rigorous Workflow & Mathematical Proof

Identify Kinematic Parameters

Select Third Equation of Motion

Solve for Height h

Conclude and Verify

360° Option Elimination Engine Key Feature

NTA Trap Alert: Dropped vs Thrown Downward

Core NEET Syllabus Standard

Ready to attempt under real exam pressure?

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