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In the absence of air resistance, a ball thrown horizontally from a tower with velocity v, will land after T seconds.
If, however, air resistance is taken into account, which statement is correct?
A: the ball lands with a horizontal velocity less than v after more than T seconds
B: the ball lands with a horizontal velocity less than v after T seconds
C: the ball lands with a horizontal velocity v after more than T seconds
D: the ball lands with a horizontal velocity v after T seconds.

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Last updated date: 01st Mar 2024
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IVSAT 2024
Answer
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Hint: The air resistance is a non-conservative force in the direction opposite to motion.
An opposition force creates deceleration on the moving body. If time taken for motion is inversely proportional to velocity of object for a fixed distance.

Complete step by step answer:
When air resistance is absent the horizontal velocity of the body is unaffected by any other external force, as the only force which acts on the ball is gravity. And as we know gravity acts downwards or in the direction towards the earth, but the horizontal velocity is perpendicular to the gravitational force and thus tends to remain unaffected.
However, when air resistance is present the situation changes. Air resistance is the force opposing the motion of a body in the atmosphere similar to viscosity experienced by a moving body in a fluid. The opposing force is non conservative in nature.
The air resistance is proportional to velocity of the body, and thus the horizontal velocity would experience a force in the direction opposite to its direction. And this force would create an acceleration in the direction opposite to the motion and reduce the velocity.
The same drag would be experienced by the vertical velocity too, though initially the vertical velocity and air resistance is zero, as time increases the velocity increases and so does air resistance which would reduce the effect of gravity.
Thus, the total time taken by the abject would increase when air resistance is present, also the horizontal velocity would decrease.

So, the correct answer is “Option A”.

Note:
The air resistance depends on velocity of the body and the surface area of the object.
As the surface increases the air resistance experienced would also increase.Streamlined shape helps in reducing the effect of air resistance.
Air resistance is the force opposing the motion of a body in the atmosphere similar to viscosity experienced by a moving body in a fluid.
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