Question

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

Short answer

Answer: (d) negative, negative

Step-by-step solution

Recall Characteristics of Projectile Motion

Ideal projectile motion is the motion of an object launched horizontally, which moves under the influence of gravity only. The object's motion can be divided into two parts: the horizontal motion and the vertical motion.

Identify the Vertical Acceleration

In ideal projectile motion, the only force acting on the object is gravity. Gravity acts vertically downward, causing the object to accelerate in the negative y-direction. This means the y-component of acceleration is always negative during both the ascending and descending parts of the motion.

Determine the Answer Choice

Since the y-component of the acceleration is always negative during both the ascending and descending parts of the motion, the correct answer is (d) negative, negative.

Key concepts

Ideal Projectile Motion

Ideal projectile motion describes the motion of an object that is projected into the air and influenced only by gravity, with no air resistance or other forces at play. It's a simplified model used to analyze the motion of objects, such as balls thrown in the air or rocks hurled from a catapult.

During the ascent and descent of a projectile, its horizontal velocity remains constant due to the absence of horizontal forces, while its vertical motion is affected solely by the force of gravity. This vertical component is what creates the classic parabolic trajectory that we commonly associate with projectiles.

Understanding the ideal projectile motion allows us to predict where and when the projectile will land, which can be crucial for various applications in sports, military, and aerospace engineering. Its analysis is based on breaking the motion into horizontal and vertical components, each of which can be described by basic kinematic equations.

Vertical Acceleration

Vertical acceleration in the context of ideal projectile motion is the rate of change of vertical velocity of the object as it moves through the air. While the projectile's horizontal motion is unaccelerated since there are no horizontal forces at work, the vertical motion experiences constant acceleration due to gravity.

As per Newton's second law, the acceleration of an object as produced by a net force is directly related to the magnitude of the force, in this case, gravity. Regardless of whether the projectile is ascending toward its highest point or descending back to the ground, the vertical acceleration remains directed downward. This is why, in our projectile motion example, the vertical component of the acceleration is always negative, reflecting the direction of gravity's pull against the positive vertical axis. It's important for students to grasp that 'negative' acceleration doesn't imply 'slowing down'—in this case, it simply indicates directionality.

Key Takeaway

Vertical acceleration is unchanging in ideal projectile motion and acts in the opposite direction of the upward motion of the projectile, continuously altering the vertical velocity until the object returns to earth.

Influence of Gravity

Gravity's influence on projectile motion is the singular force that dictates the vertical component of the motion. The constant acceleration due to gravity, approximately \[\begin{equation}9.81 \, \text{m/s}^2\end{equation}\]on Earth, is what pulls the projectile back to the ground after it is launched.

While gravity does not affect the horizontal motion of the projectile—hence the constant horizontal velocity—the vertical motion is continuously accelerated in the direction of the gravitational pull. This means that, while in flight, even as the projectile's ascent slows down, the speed at which it descends increases due to this constant acceleration. This is why objects thrown upwards will eventually come back down, even if they are launched with considerable force.

• Gravity affects the vertical speed, not the horizontal speed.
• The acceleration due to gravity is always directed towards the center of the Earth, defining the 'downward' direction in our equations.
• It is unyielding and ever-present, affecting every moment of the projectile's path.

Grasping the influence of gravity is essential in predicting the behavior of any projectile and is a cornerstone concept in physics.