A particle is hurled into air from a point on the horizontal...

Name: Problem 25, Chapter 4: Master Resource Book in JEE Main Physics
Uploaded: 2022-01-14T08:07:39-08:00
Duration: 1 min 5 s
Channel: Hast Aggarwal
Description: A particle is hurled into air from a point on the horizontal ground at an angle with the vertical. If the air exerts a constant resistive force (a) the path of projectile will be parabolic path (b) the time of ascent will be equal to time of descent (c) the total energy of the projectile is not conserved (d) at the highest point, the velocity of projectile is horizontal

A particle is hurled into air from a point on the horizontal ground at an angle with the vertical. If the air exerts a constant resistive force (a) the path of projectile will be parabolic path (b) the time of ascent will be equal to time of descent (c) the total energy of the projectile is not conserved (d) at the highest point, the velocity of projectile is horizontal

A particle is hurled into air from a point on the horizontal ground at an angle with the vertical. If the air exerts a constant resistive force
(a) the path of projectile will be parabolic path
(b) the time of ascent will be equal to time of descent
(c) the total energy of the projectile is not conserved
(d) at the highest point, the velocity of projectile is horizontal

Key Concepts

Projectile Motion

Projectile motion studies the motion of an object launched into the air subject only to gravity (in the ideal case) or other forces such as air resistance. In the absence of air resistance, the path is a parabola due to the constant acceleration downward; however, when additional forces act on the projectile, like drag, this parabolic path is altered.

Air Resistance Effects on Motion

Air resistance, or drag, is a force acting opposite to the direction of motion. When a constant resistive force is present, it affects the projectile’s motion by reducing its speed and altering its trajectory compared to ideal, drag-free motion. This force does not depend solely on speed or position, and its presence means that the motion is no longer symmetric between ascent and descent.

Energy Dissipation

The concept of energy conservation in mechanics holds that in an isolated system with only conservative forces, mechanical energy remains constant. The presence of a resistive force like air resistance is non-conservative, meaning it dissipates energy (usually as heat), so the total mechanical energy of the projectile is not conserved.

Time of Flight Asymmetry

In ideal projectile motion without air resistance, the time of ascent equals the time of descent due to symmetry. However, when air resistance is present, the decelerating effect during ascent is not exactly reversed during descent, leading to differences in the times of ascent and descent.

Velocity Components at Maximum Height

At the maximum height of a projectile's trajectory, the vertical component of velocity becomes zero, leaving only the horizontal component. This principle holds even when air resistance is present, although the magnitude of the horizontal velocity may be reduced by drag.

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