Published by:
CGP EDU Academic Team
Published on: September 12, 2026
A person standing at some distance from a high tree, throws a stone taking aim at a fruit hanging from that free, and at the same instant of time the fruit begins to fall freely. Of the following statement which is correct?
Text Solution
Verified by ExpertsThe correct answer is:
B
Step 1: Analyze the motion of the stone and the fruit.
When the person throws the stone, it moves upwards and then follows a parabolic trajectory due to the gravitational force acting on it once it leaves the hand, while the fruit starts falling freely from the tree, also under the influence of gravity.
Step 2: Understand the condition for the stone to hit the fruit.
The stone can only hit the falling fruit if it is thrown with sufficient initial velocity and the aim is correct. To determine the minimum velocity required, we can analyze the motion equations.
Step 3: Apply equations of motion.
Let the height of the fruit from the ground be $h$ and the distance from the person to the tree be $d$. The fruit falls a height $h$ under the influence of gravity with acceleration $g$. The time taken by the fruit to hit the ground is given by:
$$t = rac{ ext{sqrt}(2h/g)}$$
During the time the stone is in the air, it should travel horizontally a distance $d$ and reach the same height $h$ as the fruit. Thus, we can express the conditions for hitting the fruit in terms of its initial velocity and angle of projection.
Step 4: Conclude the condition.
If thrown with the right initial velocity and angle, the stone can intersect the path of the falling fruit, meaning the stone strikes the fruit if the stone is thrown with a definite minimum velocity.
Final conclusion:
Therefore, the correct option is B.
When the person throws the stone, it moves upwards and then follows a parabolic trajectory due to the gravitational force acting on it once it leaves the hand, while the fruit starts falling freely from the tree, also under the influence of gravity.
Step 2: Understand the condition for the stone to hit the fruit.
The stone can only hit the falling fruit if it is thrown with sufficient initial velocity and the aim is correct. To determine the minimum velocity required, we can analyze the motion equations.
Step 3: Apply equations of motion.
Let the height of the fruit from the ground be $h$ and the distance from the person to the tree be $d$. The fruit falls a height $h$ under the influence of gravity with acceleration $g$. The time taken by the fruit to hit the ground is given by:
$$t = rac{ ext{sqrt}(2h/g)}$$
During the time the stone is in the air, it should travel horizontally a distance $d$ and reach the same height $h$ as the fruit. Thus, we can express the conditions for hitting the fruit in terms of its initial velocity and angle of projection.
Step 4: Conclude the condition.
If thrown with the right initial velocity and angle, the stone can intersect the path of the falling fruit, meaning the stone strikes the fruit if the stone is thrown with a definite minimum velocity.
Final conclusion:
Therefore, the correct option is B.
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