Physics Q29 – JEE-MAIN 2026

Home Physics Motion in a Straight LineQuestion #325

A gas balloon is going up with a constant velocity of

10 m/s

. When this balloon reached a height of

75 m

, a stone is dropped from it and balloon keeps moving up with the same velocity. The height of the balloon when the stone hits the ground is _______

m

(Take

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

)

Clue 1 of 3: Relative Motion and Kinematics

Understand that when the stone is dropped, it initially possesses the velocity of the balloon. Then, it undergoes motion under gravity.

🧠 Full Solution Path

Step 1: Determine initial conditions for the stone✦ Active

When the stone is dropped from the balloon, it initially possesses the same upward velocity as the balloon. Thus, for the stone:

u_{s} = + 10 m/s

The initial height from which the stone is dropped is $h_{0} = 75 m$ . The acceleration due to gravity is $a = - g = - 10 {m/s}^{2}$ (taking upward as positive). The displacement of the stone when it hits the ground is $Δ y_{s} = - 75 m$ .

Step 2: Calculate the time for the stone to hit the ground○ Expand

Using the kinematic equation $Δ y = u t + \frac{1}{2} a t^{2}$ for the stone:

- 75 = (10) t + \frac{1}{2} (- 10) t^{2}

Simplifying the equation:

- 75 = 10 t - 5 t^{2}

Rearranging into a standard quadratic form and dividing by 5:

5 t^{2} - 10 t - 75 = 0

\Rightarrow t^{2} - 2 t - 15 = 0

Factoring the quadratic equation:

(t - 5) (t + 3) = 0

Since time cannot be negative, the time taken for the stone to hit the ground is $t = 5 s$ .

💡 Teacher's Secret Hint

Ensure correct sign conventions for displacement and acceleration.

Step 3: Calculate the final height of the balloon○ Expand

The balloon continues to move upwards with a constant velocity of $v_{b} = 10 m/s$ for the same duration $t = 5 s$ .

The additional distance covered by the balloon in this time is:

Δ h_{b} = v_{b} \times t = 10 m/s \times 5 s = 50 m

The final height of the balloon from the ground when the stone hits the ground will be its initial height plus the distance it traveled:

H_{f i n a l} = h_{0} + Δ h_{b} = 75 m + 50 m = 125 m

💡 Teacher's Secret Hint

Remember that the balloon's motion is independent of the stone's motion once the stone is dropped, except for the time duration.

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Physics Question 29 – JEE-MAIN 2026

Clue 1 of 3: Relative Motion and Kinematics

🧠 Full Solution Path