Question

Assertion: (A) If both Assertion - Reason are true, reason is correct explanation of Assertion. (B) If both Assertion - Reason are true but reason is not correct explanation of Assertion. (C) Assertion is true but Reason is false. (D) If Reason is true but Assertion is false At the highest point of projectile motion the velocity is not zero. Reason: Only the vertical component of velocity is zero. Where as horizontal component still exists. (A) a (B) \(\mathrm{b}\) (C) \(\mathrm{c}\) (D) \(\mathrm{d}\)

Short answer

The short answer for this question is: (A) Both the Assertion and Reason are true, and the Reason is the correct explanation for the Assertion.

Step-by-step solution

Identify the Assertion and Reason

The Assertion is the claim "At the highest point of projectile motion the velocity is not zero." The Reason given here is "Only the vertical component of velocity is zero. Whereas horizontal component still exists."

Analyse the Assertion

The Assertion claims that at the highest point of a projectile's motion, the velocity is not zero. This is correct. When a projectile is at its highest point, its vertical velocity component is indeed zero; however, its horizontal velocity remains constant due to the absence of any horizontal forces (in case of neglecting air resistance). Hence, the full velocity of the projectile (a vector quantity) is not zero.

Analyse the Reason

The Reason provided is "Only the vertical component of velocity is zero. Whereas horizontal component still exists." This statement is also true. When a projectile is at its peak, the upward motion decreases to zero due to gravity, resulting in a zero vertical velocity. Nonetheless, the absence of any horizontal force keeps the horizontal velocity constant.

Assess if Reason provides a correct explanation of Assertion

The Reason states the exact factors causing the situation described in the Assertion, explaining that only the vertical component of velocity is zero, while the horizontal component still exists. Hence, the Reason provides an accurate explanation for why the velocity of a projectile is not zero at its highest point. So the answer to the given exercise is: (A) Both the Assertion and Reason are true, and the Reason is the correct explanation for the Assertion.

Key concepts

Velocity Components

Projectile motion is a fascinating concept in physics, where an object moves along a curved path under the influence of gravity. The object's complete velocity is a combination of two main components: horizontal and vertical. These "velocity components" are fundamental in understanding how an object behaves when thrown or projected.
Each component acts independently of the other. The horizontal component deals with the sideways motion, while the vertical component takes care of the up-and-down movement. The mastery of these concepts helps explain how projectiles move through air, making it essential for solving problems in projectile motion. Without considering both components, we wouldn't fully understand or predict the trajectory of a projectile. By analyzing these components separately, we can gain insights into the complete movement and characteristics of any projectile.

Horizontal Velocity

Horizontal velocity is the component that helps the projectile move sideways. Imagine you're throwing a frisbee or a ball; the force you exert on it horizontally plays a significant role in its path.
This velocity component remains constant throughout the motion, assuming there's no air resistance. That's because there are usually no horizontal forces acting on the projectile, allowing it to maintain a steady speed. This is unlike vertical velocity, which changes because of gravity.
Tracking horizontal velocity is crucial because it tells you how far and how fast the projectile will travel sideways. If you're trying to hit a target at a certain distance, mastering this can help you aim accurately.

Vertical Velocity

Vertical velocity is all about the up and down motion of the projectile. It's influenced by gravity, which plays a big role in changing this velocity component.
When you throw an object upward, it fights against gravity, which slows it down until it stops momentarily at the highest point. At this point, the vertical velocity is zero. But shortly after, gravity pulls it back down, increasing the vertical speed downward.
Understanding vertical velocity is key to knowing how high an object will go and how long it stays in the air. This component is constantly changing, unlike the horizontal velocity, because of gravity's interference.

Physics Problem Solving

Physics problem solving in projectile motion involves breaking down the motion into its key components, analyzing each individually to get a complete picture of the object's path.
We often start by identifying all known values, such as initial speed, angle of projection, and forces acting on the object. Then, by applying equations of motion, we can predict how the projectile will behave.

• Consider horizontal and vertical components separately.
• Use the right equations for each component.
• Remember that the sum of the two components gives you the total velocity at any point.
• Pay attention to the forces affecting each component, with gravity impacting vertical movement and usually no force affecting horizontal travel.

Approaching problems with these steps ensures a structured path to the solution, making it easier to tackle complex scenarios.