JEE 2026 Physics Question.

Welcome back, students!
In today’s tutorial, we’ll be solving one of the most challenging physics questions on projectile motion — specifically focused on how maximum height relates to time of flight. This is one of the trickiest but most examinable topics in JEE Physics.

Let’s break it down step by step.

You can watch the full class in the video below:

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Question: Comparing the Time of Flight of Two Balls

Problem Statement:
Two balls with the same mass and the same initial velocity are projected at different angles. The maximum height reached by the first ball is eight times higher than that of the second ball.

Let:

• T1T_1T1​ = total flight time of the first ball
• T2T_2T2​ = total flight time of the second ball

Find the ratio T1T2\frac{T_1}{T_2}T2​T1​​

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Step-by-Step Explanation:

We are told:

• Mass is the same
• Initial velocity is the same
• H1=8H2H_1 = 8H_2H1​=8H2​

Now, we know the formula for maximum height in projectile motion: H=u2sin⁡2θ2gH = \frac{u^2 \sin^2 \theta}{2g}H=2gu2sin2θ​

For the two balls, this becomes: u2sin⁡2θ12g=8×u2sin⁡2θ22g\frac{u^2 \sin^2 \theta_1}{2g} = 8 \times \frac{u^2 \sin^2 \theta_2}{2g}2gu2sin2θ1​​=8×2gu2sin2θ2​​

Cancel u2u^2u2 and 2g2g2g from both sides: sin⁡2θ1=8sin⁡2θ2\sin^2 \theta_1 = 8 \sin^2 \theta_2sin2θ1​=8sin2θ2​

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Now Calculate Time of Flight

Recall that time of flight is given by: T=2usin⁡θgT = \frac{2u \sin \theta}{g}T=g2usinθ​

So, T1=2usin⁡θ1g,T2=2usin⁡θ2gT_1 = \frac{2u \sin \theta_1}{g}, \quad T_2 = \frac{2u \sin \theta_2}{g}T1​=g2usinθ1​​,T2​=g2usinθ2​​

Now take the ratio: T1T2=sin⁡θ1sin⁡θ2\frac{T_1}{T_2} = \frac{\sin \theta_1}{\sin \theta_2}T2​T1​​=sinθ2​sinθ1​​

From the previous result: sin⁡2θ1=8sin⁡2θ2⇒sin⁡θ1sin⁡θ2=8=22\sin^2 \theta_1 = 8 \sin^2 \theta_2 \Rightarrow \frac{\sin \theta_1}{\sin \theta_2} = \sqrt{8} = 2\sqrt{2}sin2θ1​=8sin2θ2​⇒sinθ2​sinθ1​​=8​=22​

Final Answer: T1T2=22\frac{T_1}{T_2} = \boxed{2\sqrt{2}}T2​T1​​=22​​

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Watch more educational videos and past questions: https://youtube.com/@allcbts

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Why This Question Matters for JEE

This problem touches on several high-yield physics concepts:

• Projectile motion
• Time of flight & maximum height formulas
• Trigonometric identities
• Ratio simplification

These are all frequently tested in JEE Main and Advanced Physics exams.

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Master JEE Physics with this step-by-step solution to a projectile motion question. Learn how to relate maximum height to time of flight — a key concept in JEE 2025 Physics.

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JEE 2025 Physics, projectile motion JEE, time of flight formula, JEE past questions physics, maximum height projectile, trigonometry in motion, jee advanced problems