AP Physics B Kinematics Presentation #77

The New Jersey Center for Teaching and Learning
26 Jun 201204:37
EducationalLearning
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TLDRThe script explains the physics of a ball thrown at 8 m/s at a 35° angle, undergoing projectile motion. It emphasizes that horizontal velocity remains constant throughout the motion, while the vertical component changes direction but maintains the same magnitude due to no net work being done in the vertical direction. The key takeaway is that the speed of the ball when it returns to the original horizontal level is the same as the initial speed, which is 8 m/s, as demonstrated through the equations of motion.

Takeaways
  • 🚀 The ball is thrown with an initial speed of 8 m/s at a 35° angle above the horizontal.
  • 📏 The problem focuses on the speed of the ball when it returns to the same horizontal level, ignoring direction.
  • 🔄 The horizontal velocity (Vx) remains constant throughout the motion due to no acceleration in the horizontal direction.
  • 🔽 The vertical velocity (Vy) changes in direction but not in magnitude from the initial to the final position.
  • 📐 The formula V^2 = u^2 + 2as is used to analyze the vertical component of the velocity, where 'a' is acceleration and 's' is displacement.
  • ⏱ At the initial and final positions, the vertical displacement (Δy) is zero, simplifying the equation to Vf^2 = Vi^2 for the vertical component.
  • 🔃 The final vertical velocity (Vfy) is equal in magnitude but opposite in direction to the initial vertical velocity (Viy).
  • 🔢 The magnitude of the final velocity (Vf) is calculated using the Pythagorean theorem, Vf = √(Vx^2 + Vfy^2).
  • 🔄 The final velocity's magnitude is shown to be the same as the initial velocity's magnitude, which is 8 m/s.
  • 🎯 The conclusion is that the speed of the ball when it returns to the same horizontal level is also 8 m/s, demonstrating that the initial and final speeds are equal.
Q & A

  • What is the initial speed of the ball when thrown?

    -The initial speed of the ball is 8 m/s.

  • At what angle is the ball thrown above the horizontal?

    -The ball is thrown at an angle of 35° above the horizontal.

  • What is the significance of the horizontal velocity (Vx) in projectile motion?

    -The horizontal velocity (Vx) remains constant throughout the projectile motion because there is no acceleration in the horizontal direction.

  • Why does the vertical velocity (Vy) change during the projectile motion?

    -The vertical velocity (Vy) changes due to the acceleration due to gravity acting on the ball, causing it to slow down as it ascends and speed up as it descends.

  • What is the formula used to relate the initial and final vertical velocities?

    -The formula used is V^2 = u^2 + 2 * a * Δy, where V is the final vertical velocity, u is the initial vertical velocity, a is the acceleration due to gravity, and Δy is the change in vertical position.

  • Why is the final vertical velocity (Vfy) negative when the ball returns to the same horizontal level?

    -The final vertical velocity (Vfy) is negative because it is in the downward direction, opposite to the initial upward direction of the throw.

  • How does the magnitude of the final velocity compare to the initial velocity?

    -The magnitude of the final velocity is the same as the initial velocity because the changes in vertical velocity due to gravity are symmetrical during the ascent and descent.

  • What does it mean for the speed of the ball to be the same when it returns to the same horizontal level?

    -It means that the magnitude of the velocity, or the speed, is the same at the beginning and end of the projectile motion, which is 8 m/s in this case.

  • Why is the horizontal component of the velocity (Vx) not affected by gravity?

    -The horizontal component of the velocity (Vx) is not affected by gravity because gravity acts vertically, and there is no horizontal acceleration.

  • What is the role of the angle of projection in determining the path of the ball?

    -The angle of projection determines the initial vertical and horizontal components of the velocity, which in turn dictate the trajectory of the ball in projectile motion.

  • How does the script demonstrate that the initial and final velocities are equal in magnitude?

    -The script uses the equations V^2 = u^2 + 2 * a * Δy and Vf = √(Vx^2 + Vfy^2) to show that the initial and final velocities have the same magnitude, considering the symmetry of the vertical motion.

Outlines
00:00
🚀 Projectile Motion and Velocity Analysis

This paragraph discusses the physics of a ball thrown at an initial speed of 8 m/s at a 35° angle to the horizontal. It explains that the horizontal component of the velocity (Vx) remains constant throughout the projectile's trajectory due to no acceleration in the horizontal direction. The vertical component (Vy), however, changes due to gravity, but when the ball returns to its original horizontal level, the magnitude of the vertical velocity is the same as at the start, just in the opposite direction. The paragraph uses kinematic equations to demonstrate that the speed of the ball when it returns to the original level is the same as the initial speed, concluding that the magnitude of the final velocity is 8 m/s.

Mindmap
Keywords
💡Projectile Motion
Projectile motion is the motion of an object thrown or projected into the air, where it moves along a curved path under the action of gravity alone. In the video, the ball's motion is described as projectile motion, which is the central theme of the discussion. The script explains how the ball follows a parabolic trajectory when thrown at an angle to the horizontal.
💡Initial Speed
Initial speed refers to the speed at which an object is launched in projectile motion. In the context of the video, the ball is thrown with an initial speed of 8 m/s. This speed is a critical factor in determining the ball's trajectory and is used to calculate its velocity components in both the horizontal and vertical directions.
💡Angle of Projection
The angle of projection is the angle at which a projectile is launched relative to the horizontal. The video mentions a 35° angle above the horizontal, which affects the vertical and horizontal components of the initial velocity, and thus the overall trajectory of the ball.
💡Horizontal Velocity
Horizontal velocity, denoted as "V_x" in the script, is the component of the velocity of a projectile that is parallel to the ground. The video emphasizes that horizontal velocity remains constant throughout the motion because there is no acceleration in the horizontal direction, which is a key concept in understanding projectile motion.
💡Vertical Velocity
Vertical velocity, represented as "V_y" in the script, is the component of the velocity of a projectile that is perpendicular to the ground. The script discusses how the vertical velocity changes due to gravity, affecting the height the ball reaches and its return to the same horizontal level.
💡Velocity Components
Velocity components refer to the separate horizontal and vertical speeds of a moving object, in this case, the ball. The video script breaks down the initial velocity into its horizontal and vertical components to analyze the ball's motion and to demonstrate that the magnitude of the final velocity is the same as the initial velocity.
💡Magnitude of Velocity
The magnitude of velocity is the speed of an object, which is the length of the velocity vector. The video script uses the term to explain that the speed of the ball when it returns to the same horizontal level is the same as the initial speed, which is 8 m/s, as the magnitude of the velocity remains constant in projectile motion without air resistance.
💡Free Fall
Free fall is the motion of an object falling under the force of gravity alone, without any other forces acting on it. The script indirectly refers to this concept when discussing the vertical component of the ball's motion, which behaves like a free-falling object when it is not being thrown upwards.
💡Equation of Motion
The equation of motion, specifically "V^2 = v^2 + 2aΔy", is used in the script to relate the initial and final vertical velocities of the ball. It is a fundamental equation in physics that describes how the final velocity of an object is determined by its initial velocity, the acceleration, and the change in position in the direction of the acceleration.
💡Parabolic Trajectory
A parabolic trajectory is the path followed by a projectile under the influence of gravity, without air resistance. The video script describes the ball's path as parabolic, which is a key visual element in understanding the motion of the ball from the throw to its return to the same horizontal level.
💡Final Velocity
Final velocity is the speed of an object at the end of its motion. In the video, the script concludes that the magnitude of the final velocity of the ball when it returns to the ground is the same as the initial velocity, which is a result of the conservation of energy in an ideal projectile motion scenario.
Highlights

A ball is thrown at an original speed of 8 m/s at an angle of 35° above the horizontal.

The problem involves determining the speed of the ball when it returns to the same horizontal level.

Projectile motion is considered, with the ball following a parabolic trajectory.

Horizontal velocity (Vx) remains constant throughout the motion due to no acceleration in the horizontal direction.

The vertical component of velocity (Vy) changes due to gravity, affecting the ball's motion upwards and downwards.

The final vertical velocity (Vfy) is equal in magnitude but opposite in direction to the initial vertical velocity (Vy).

The formula V^2 = u^2 + 2as is used to analyze the vertical component of the velocity.

Since the ball starts and ends at the same height, the change in vertical position (Δy) is zero.

The final vertical velocity squared is equal to the initial vertical velocity squared, indicating no change in magnitude.

The magnitude of the final velocity is the same as the initial velocity due to the conservation of kinetic energy in the vertical direction.

The final velocity (Vf) is calculated using the Pythagorean theorem, Vf = √(Vx^2 + Vy^2).

The horizontal component of the final velocity (Vfx) remains the same as the initial horizontal velocity (Vx).

The vertical component of the final velocity (Vfy) is the negative of the initial vertical velocity (Vy) due to gravity.

The magnitude of the velocity at the final position is demonstrated to be the same as the initial velocity.

The answer to the problem is that the speed of the ball when it returns to the same horizontal level is 8 m/s.

The demonstration of the velocity's conservation is shown through two key equations relating initial and final velocities.

The problem concludes that the speed of the ball remains constant at 8 m/s throughout its trajectory.

Transcripts

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Projectile MotionPhysicsVelocityHorizontalAngleSpeedMotion AnalysisThrowingLandingEducational