(Part 1 of 2) An Introductory Projectile Motion Problem with an Initial Horizontal Velocity

Flipping Physics
21 Apr 201409:41
EducationalLearning
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TLDRIn the video, Mr. P and his students tackle a projectile motion problem involving a ball dropped from a moving car. They calculate the horizontal displacement required for the ball to land in a bucket, using the principles of uniformly accelerated motion and constant velocity in the x-direction. Through this engaging problem-solving process, they highlight the impact of variables like air resistance and car speed on the experiment's precision.

Takeaways
  • 📚 The problem discussed is a projectile motion problem with an object having an initial horizontal velocity.
  • 🚗 The scenario involves a car moving at 10.0 miles per hour where a ball is dropped from a height of 0.70 meters above the top of a bucket.
  • 🎯 The goal of Part One is to determine the distance from which the ball should be dropped to land in the bucket.
  • 📐 The ball's motion is split into x and y components, with the x-component having a constant velocity and the y-component undergoing free-fall.
  • 📌 Known values include a y-displacement of -0.70 meters, a y-acceleration of -9.81 m/s², and an x-velocity conversion from 10 miles per hour to 4.4694444 meters per second.
  • ⏱️ The change in time (0.377772 seconds) is calculated using the y-motion, which is then used for the x-motion calculations.
  • 📊 The calculated displacement in the x direction is 1.68843 meters, rounded to 1.7 meters for practical purposes.
  • 🚀 The experiment showed that the actual displacement was slightly off due to the car's speed and the difficulty in timing the ball release.
  • 🌬️ Air resistance was noted as a factor, but the car's speed had a more significant impact on the ball's x-displacement.
  • 🔍 The problem is not fully solved as the final velocity of the ball before striking the bucket will be discussed in a subsequent lesson.
  • 🤔 The lesson highlights the complexities of real-world experiments and the importance of controlling variables.
Q & A

  • What type of motion is being discussed in the script?

    -Projectile motion is being discussed, specifically focusing on an object with an initial horizontal velocity.

  • What is the initial velocity of the ball in the x-direction?

    -The initial velocity of the ball in the x-direction is 10.0 miles per hour, which is later converted to 4.4694444 meters per second.

  • How is the height from which the ball is dropped related to the problem?

    -The height of 0.70 meters is the displacement in the y-direction and is used to calculate the time it takes for the ball to fall, which is then used to find the horizontal displacement.

  • What is the acceleration in the y-direction?

    -The acceleration in the y-direction is negative 9.81 meters per second squared, which represents the acceleration due to gravity.

  • Why is the initial velocity in the y-direction zero?

    -The initial velocity in the y-direction is zero because the ball is not moving up or down before it is dropped.

  • How is the change in time calculated?

    -The change in time is calculated using the equation for uniformly accelerated motion in the y-direction: 2 * (negative 0.7 meters) equals negative 9.81 m/s^2 times the change in time squared. Taking the square root of this equation gives a change in time of approximately 0.377772 seconds.

  • What is the displacement in the x-direction that the ball should be dropped from the bucket?

    -The ball should be dropped 1.7 meters in front of the bucket to land in it, calculated using the horizontal velocity and the change in time.

  • What factor was mentioned to have a larger effect on the ball's displacement in the x-direction than air resistance?

    -The speed of the car has a larger effect on the ball's displacement in the x-direction than air resistance.

  • How does the speed of the car affect the displacement in the x-direction?

    -If the speed of the car is decreased by half a mile per hour, the displacement in the x-direction of the ball decreases by more than eight centimeters.

  • What was the main difficulty in the experiment?

    -The main difficulty in the experiment was controlling the speed of the car and releasing the ball at the right time.

  • What is the purpose of the next lesson after this problem?

    -The purpose of the next lesson is to determine the final velocity of the ball just before it strikes the bucket.

Outlines
00:00
📚 Introduction to Projectile Motion

In this introductory lesson on projectile motion, Mr. P sets up a scenario where an object is dropped from a car moving at a constant horizontal velocity. The goal is to determine the displacement in the x direction. The class engages in a collaborative discussion, identifying known values and the need to split the motion into x and y components. The problem involves a ball dropped from a height of 0.70 meters in a car moving at 10.0 miles per hour, aiming to land in a bucket. The students, Bo, Billy, and Bobby, contribute to the discussion, clarifying that the initial velocity in the y direction is zero, and the acceleration due to gravity is -9.81 m/s^2. They also convert the car's velocity from miles per hour to meters per second to facilitate calculations. The paragraph concludes with a setup for the next steps in solving the problem.

05:01
🕒 Solving for Time and Displacement

This paragraph focuses on solving for the change in time, which is a critical step in addressing the projectile motion problem. The class recognizes the need to find a change in time due to its scalar nature, allowing its application in both directions of motion. Billy uses the kinematic equation for displacement in the y direction to find the change in time, resulting in 0.377772 seconds. With the time determined, the class then applies the velocity-time relationship in the x direction to calculate the required displacement for the ball to land in the bucket. The calculation yields a result of 1.7 meters, which is later validated through a physical experiment. However, Mr. P notes that while air resistance and car speed introduce minor and major variations respectively, the experiment's imprecision lies in controlling the car's speed and the timing of the ball release. The paragraph ends with Mr. P teasing the next lesson, which will address determining the ball's final velocity before impact.

Mindmap
Keywords
💡Projectile Motion
Projectile motion refers to the motion of an object that is launched into the air and moves under the influence of gravity and air resistance. In the video, the ball dropped from the car exemplifies projectile motion as it is subject to gravity pulling it downwards while also moving horizontally at the initial velocity of the car. This concept is central to solving the problem of where to drop the ball so it lands in the bucket.
💡Displacement
Displacement is a vector quantity that represents the change in position of an object, having both magnitude and direction. In the context of the video, displacement is crucial for determining how far the ball moves in both the x (horizontal) and y (vertical) directions. The problem's goal is to find the horizontal displacement that allows the ball to land in the bucket.
💡Acceleration
Acceleration is the rate of change of velocity of an object with respect to time, and in the video, it specifically refers to the acceleration due to gravity, which is acting on the ball in the y direction. The negative value indicates that the acceleration is downward. Understanding acceleration is key to analyzing the ball's motion and solving for its displacement.
💡Uniformly Accelerated Motion
Uniformly Accelerated Motion (UAM) is a type of motion where an object's acceleration remains constant. In the video, the ball is in UAM in the y direction because it experiences a constant acceleration due to gravity, allowing the use of UAM equations to solve for the displacement in that direction.
💡Velocity
Velocity is a vector quantity that describes the speed of an object in a specific direction. In the context of the video, the ball has an initial horizontal velocity due to the car's motion, and its vertical velocity changes due to gravity. The final velocity of the ball is also a topic of interest for the next lesson.
💡Free-Fall
Free-fall is a type of motion where an object is subject only to gravity, with no other forces acting on it (ignoring air resistance). In the video, the ball is in free-fall in the y direction after being dropped from the car, as it is only influenced by gravity's acceleration.
💡Air Resistance
Air resistance is the force that opposes the motion of an object through the air. Although it is not the primary focus of the problem, the video briefly mentions that air resistance could affect the ball's motion, but its impact is relatively small compared to the car's speed.
💡Scalar
A scalar is a quantity that has magnitude but no direction. In the video, change in time is an example of a scalar, which means it can be used in calculations regardless of the direction of motion. The concept of scalars is important for understanding how the change in time applies to both the x and y directions of the ball's motion.
💡Change in Time
Change in time refers to the difference in time before and after an event. In the video, determining the change in time is essential for calculating the displacement in both the x and y directions. It is found by using the equations of motion for the ball's projectile motion.
💡Conversion of Units
The conversion of units is the process of changing a physical quantity from one unit of measurement to another. In the video, the car's speed is initially given in miles per hour, and it needs to be converted to meters per second to match the units used in the calculations. This conversion is necessary for accurate problem-solving.
💡Experiment
An experiment is a scientific procedure conducted to support, refute, or validate a hypothesis by obtaining empirical evidence. In the video, the students perform a real-world experiment to test their theoretical calculations and see if the ball lands in the bucket as predicted by their projectile motion analysis.
Highlights

Introduction to projectile motion problem with an object having an initial horizontal velocity.

The problem involves a ball dropped from a car moving at 10.0 miles per hour, from a height of 0.70 meters above a bucket.

The objective is to find out where to drop the ball so that it lands in the bucket.

The ball is in projectile motion, moving through a two-dimensional space.

Known values are listed for both x and y directions, emphasizing the importance of separating variables for each dimension.

The conversion of velocity from miles per hour to meters per second is discussed, highlighting the importance of unit consistency.

The calculation of the ball's velocity in the x-direction is performed, resulting in 4.4694444 meters per second.

The initial velocity in the y direction is determined to be zero, as the ball is not moving up or down before being dropped.

The displacement in the x direction is the unknown we are trying to find, which is a key part of the problem.

The change in time, a scalar, is identified as a crucial factor to solve for next, due to known variables in the y direction.

The equation for uniformly accelerated motion in the y direction is used to find the change in time, resulting in 0.377772 seconds.

The change in time, being a scalar, is then applied to the x direction to calculate the displacement.

The displacement in the x direction is calculated to be 1.7 meters, indicating where to drop the ball for it to land in the bucket.

An experiment is conducted to test the theory, with the ball being dropped in an attempt to land it in the bucket.

Air resistance is acknowledged as a factor that could affect the outcome, but it is determined to have a minimal impact on the displacement.

The speed of the car is identified as having a significant effect on the ball's displacement in the x direction, more so than air resistance.

The difficulty in controlling the car's speed and the timing of dropping the ball is discussed as a challenge in the experiment.

The lesson concludes with a successful, though not perfect, experiment and an introduction to the next problem involving the ball's final velocity before impact.

Transcripts

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PhysicsExperimentProjectileMotionEducationalFunClassroomSceneProblemSolvingDimensionalAnalysisAccelerationDueToGravityVelocityConversionAirResistanceImpreciseMeasurements