Question

In ideal projectile motion, when the positive \(y\) -axis is chosen to be vertically upward, the \(y\) -component of the velocity of the object during the ascending part of the motion and the \(y\) -component of the velocity during the descending part of the motion are, respectively, a) positive, negative. c) positive, positive. b) negative, positive. d) negative, negative.

Short answer

Answer: The y-components of the velocity during the ascending and descending parts of an object in ideal projectile motion are positive and negative, respectively. This is because the object is moving upward against the force of gravity during the ascending part, and downward due to the force of gravity during the descending part.

Step-by-step solution

Analyze the ascending part of the motion

During the ascending part, the object is moving upward against the force of gravity. As a result, the y-component of the velocity is decreasing, but the object is still moving upward, so the velocity is positive.

Analyze the descending part of the motion

During the descending part, the object is moving downward due to the force of gravity. Hence, the y-component of the velocity is increasing in the downward direction, meaning it is negative.

Identify the correct option

Based on the analysis above, the y-component of the velocity during ascending is positive, and during descending, it is negative. Therefore, the correct option is: a) positive, negative.

Key concepts

Velocity Components

In projectile motion, velocity can be understood through its components: horizontal and vertical. The projectile’s velocity is not just a single speed but made up of these two parts working together.

• **Horizontal Component**: This remains constant throughout the motion if we ignore air resistance; it doesn't change because no force acts horizontally in ideal conditions.
• **Vertical Component**: This changes during the motion due to the force of gravity. As the object ascends, this component decreases, and as it descends, it increases negatively.

The initial velocity vector can be split into these components using trigonometry, especially by knowing the angle of projection. These components help predict the projectile’s path and are crucial in understanding how the projectile travels through the air.

Ascending and Descending Motion

The motion of a projectile can be divided into two primary phases: ascending and descending, which are critically governed by gravity. During **ascending motion**:

• The projectile moves against gravity. Its vertical component of velocity decreases until it reaches the peak.
• At the peak, this vertical velocity becomes zero, marking the transition from ascending to descending.

In the **descending motion**:

• The projectile moves in the same direction as gravity. The vertical component of velocity becomes negative and begins to increase in magnitude.
• This phase continues until the projectile impacts the ground.

This cyclical nature highlights how gravity uniquely affects each phase of projectile motion.

Force of Gravity

Gravity is a crucial force in projectile motion. It consistently acts downward, influencing both ascending and descending parts of the motion.

• **On Ascending**: Gravity slows down the upward motion, reducing the vertical velocity until motion stops at the peak.
• **On Descending**: Gravity accelerates the object downward, increasing the negative vertical velocity component.

The gravitational force remains constant throughout the motion, which makes the change in velocity predictable. Its role in creating a symmetrical path for many projectiles is why understanding gravity is vital in calculating accurate motion paths. This predictability only breaks in real-world scenarios where air resistance and other forces come into play. However, in an ideal scenario often studied in physics, gravity is the sole vertical force affecting motion.