Question

A ball is thrown vertically upward. What is the velocity and acceleration of the ball at the maximum height? (A) \(-\) gt \(\mathrm{ms}^{-1}, 0\) (B) \(0,-9 \mathrm{~ms}^{-2}\) (C) \(\mathrm{g} \mathrm{ms}^{-1}, 0\) (D) \(0,-\mathrm{gt} \mathrm{ms}^{-2}\)

Short answer

The short answer is: At the maximum height, the velocity of the ball is 0 m/s and the acceleration remains constant due to gravity, which is -9 m/s². Therefore, the correct answer is (B) \(0, -9 \mathrm{~ms}^{-2}\).

Step-by-step solution

Understanding the concepts of velocity and acceleration

In vertical motion, velocity is the rate at which an object changes its position, and acceleration is the rate at which its velocity changes. For a ball thrown vertically upward, its initial velocity is positive (since it is thrown upward) and the acceleration is negative due to gravity (-9.81 m/s², approximated to -9 m/s² for simplicity).

Finding the final velocity at the maximum height

When the ball reaches its maximum height, its final velocity becomes 0 m/s because it stops going upward and then begins to fall back down to the ground. So, the velocity of the ball at the maximum height is 0 m/s.

Identifying the acceleration at the maximum height

Gravity is the force responsible for the downward acceleration of the ball. At all times during the ball's flight, including at the maximum height, gravity is affecting it. As a result, the acceleration at the maximum height remains constant at -9 m/s².

Finding the correct answer option

After analyzing the problem and determining the velocity and acceleration at the maximum height, we match our findings with the given options: - Velocity: 0 m/s - Acceleration: -9 m/s² The correct answer is (B) \(0, -9 \mathrm{~ms}^{-2}\).

Key concepts

Understanding Velocity in Projectile Motion

Velocity is a crucial concept in understanding how objects move, especially during projectile motion. It refers to the speed of an object in a specific direction. When a ball is thrown vertically upward, its velocity is initially positive since it is moving away from the ground. However, as it climbs higher, gravity works against this upward motion, slowing the ball until it momentarily stops at its maximum height.
At the peak, the velocity of the ball reaches 0 m/s. This zero velocity indicates that the ball has reached its highest point. Beyond this point, gravity accelerates the ball downward, increasing its velocity in the opposite direction. For students learning projectile motion, it's important to grasp that velocity is not just about speed but also direction. Positive velocity indicates upward motion, while negative velocity indicates downward motion.

Acceleration and Its Role in Motion

Acceleration measures how quickly the velocity of an object changes. In vertical projectile motion, acceleration plays a critical role as it is primarily influenced by gravity's pull. As a standard rule in physics, when an object is thrown upward, the acceleration due to gravity is constant and acts downward.

• This constant acceleration is approximately \(-9.81 \text{ m/s}^2\) but is often simplified to \(-9 \text{ m/s}^2\) for ease of calculation.
• Even as the ball reaches its maximum height, where its velocity is 0, the acceleration remains at \(-9 \text{ m/s}^2\).

This consistent downward pull is what eventually brings the ball back down to Earth after reaching its peak. Acceleration being negative indicates it's counteracting the initial upward force, slowing the ball, and reversing its motion.

Gravity's Universal Influence

Gravity is a universal force that affects all objects with mass, pulling them toward the center of the Earth. In the context of projectile motion, gravity is the force responsible for both the deceleration of an object moving upwards and the acceleration of a falling object.
When a ball is thrown into the air, gravity "fights" against its upward journey from the moment it leaves the thrower's hand. The gravitational pull is a constant \(-9.81 \text{ m/s}^2\), guiding how rapidly the object's velocity changes.

• At the top of its arc, gravity ensures the velocity becomes \(0\), marking the start of the descent.
• As the ball descends, gravity continues to increase its downward velocity uniformly.

This unyielding force has a significant impact on all forms of motion and is a fundamental concept for students to understand in physics. Having a sound understanding of gravity helps demystify why all objects, regardless of their initial speed, eventually return to the ground.