Nerd-A-Pult - An Introductory Projectile Motion Problem

Flipping Physics
23 May 201409:32
EducationalLearning
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TLDRIn this entertaining physics lesson, Mr. P uses a Nerd-A-Pult to launch a ball and engage his students in solving an introductory projectile motion problem. The class works together to calculate the ball's trajectory, determining the horizontal displacement and the required vertical placement of a basket to catch the ball. Through problem-solving and the application of physics principles, they successfully calculate the ball's path, only to humorously discover that the ball bounces back out of the basket in a dramatic slow-motion demonstration.

Takeaways
  • 🎯 The Nerd-A-Pult is used for an Introductory Projectile Motion Problem in the video.
  • 🚀 The ball is launched with an initial speed of 3.25 meters per second at an angle of 61.7 degrees above the horizontal.
  • 🏀 The objective is to find the vertical placement of a basket to catch the ball after it travels 93 centimeters horizontally.
  • 📐 The initial velocity is decomposed into x and y components using trigonometric functions (sine and cosine).
  • 🕒 The x-direction problem is solved first to find the change in time, which is a scalar and applies to both directions.
  • 📈 The y-direction displacement is calculated using the uniformly accelerated motion equation with the found change in time.
  • 📊 The calculated displacement in the y-direction is -0.059785 meters, indicating the basket should be 6.0 centimeters below the launch point.
  • 🌟 The practical demonstration shows that the theoretical calculation works in real-world conditions.
  • 🤓 The video emphasizes the importance of breaking down complex problems into manageable components.
  • 📚 The problem-solving process involves drawing a picture, listing known values, and applying appropriate equations.
  • 🎓 The lesson concludes with a review, reinforcing the steps taken to solve the projectile motion problem.
Q & A

  • What is the Nerd-A-Pult used for in the video?

    -The Nerd-A-Pult is used to demonstrate an Introductory Projectile Motion Problem.

  • Where did Mr. P purchase the Nerd-A-Pult?

    -Mr. P purchased the Nerd-A-Pult from Karl and Mary Houser of Ancient Artillery.

  • What was the original purpose of the Nerd-A-Pult?

    -The Nerd-A-Pult was originally intended to launch marshmallows.

  • How was the ball launched in the problem?

    -The ball was launched with an initial speed of 3.25 meters per second at an angle of 61.7 degrees above the horizontal.

  • What is the horizontal distance between the ball's launch point and the basket?

    -The horizontal distance is 93 centimeters.

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

    -The initial velocity in the y-direction is 2.86155 meters per second, calculated using the sine of the launch angle.

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

    -The initial velocity in the x-direction is 1.54079 meters per second, calculated using the cosine of the launch angle.

  • How did they determine the change in time for the projectile motion?

    -They used the constant velocity in the x-direction and the x-displacement to calculate the change in time, which is a scalar and applies to both directions.

  • What is the vertical displacement of the ball after traveling 93 centimeters horizontally?

    -The vertical displacement is -0.059785 meters, meaning the basket needs to be 6.0 centimeters below the launch point for the ball to land in it.

  • What was the outcome of the experiment?

    -The ball landed in the basket, but it bounced back out, indicating that the calculations were correct but the ball's interaction with the basket was not perfectly elastic.

  • What did the group do to review and understand the problem better?

    -They drew a picture, listed everything they knew in both x- and y-directions, broke the initial velocity into its components, solved for the change in time, and then used that to find the displacement in the y-direction.

Outlines
00:00
🚀 Introduction to Projectile Motion with Nerd-A-Pult

This paragraph introduces the Nerd-A-Pult, a device used for an introductory lesson on projectile motion. Mr. P explains that the Nerd-A-Pult was purchased from Karl and Mary Houser and is typically used to launch marshmallows, but has been modified to launch a ball for the purpose of this problem. The problem involves launching a ball with an initial speed of 3.25 meters per second at an angle of 61.7 degrees and determining the vertical placement of a basket 93 centimeters away horizontally from the launch point. The characters engage in a discussion to clarify the known values and the approach to solve for the displacement in the y-direction.

05:05
🧠 Solving the Projectile Motion Problem

In this paragraph, the characters proceed to solve the projectile motion problem. They start by discussing the initial velocity components in both x and y directions, using trigonometric functions. They calculate the time of flight by utilizing the constant velocity in the x-direction and then apply this to the y-direction to find the vertical displacement. The solution indicates that the basket should be placed 6.0 centimeters below the launch point. The group then moves outside to test the solution in a practical demonstration, which, despite a successful launch, ends with the ball being rejected by the basket.

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 launched from the Nerd-A-Pult exemplifies projectile motion as it travels through the air, influenced by gravity pulling it downward and air resistance affecting its speed.
💡Initial Velocity
Initial velocity is the speed at which an object begins its motion. In the context of the video, the ball has an initial velocity of 3.25 meters per second at a 61.7-degree angle above the horizontal. This velocity is then broken down into its horizontal (x-direction) and vertical (y-direction) components to analyze the motion separately along each axis.
💡Acceleration
Acceleration is the rate of change of velocity of an object with respect to time. In projectile motion, the only acceleration acting on the object is the acceleration due to gravity, which is directed downward and has a value of approximately 9.81 meters per second squared. This acceleration affects the vertical motion (y-direction) of the ball, causing it to speed up as it falls towards the ground.
💡Displacement
Displacement refers to the change in position of an object. It is a vector quantity that considers both the magnitude and direction of the movement. In the video, the horizontal displacement is given as 93 centimeters, and the problem requires finding the vertical displacement where the ball should land to fall into the basket.
💡Nerd-A-Pult
The Nerd-A-Pult is a device used to launch objects, originally designed for launching marshmallows but in this context, modified to launch a ball for the projectile motion problem. It is used as a practical tool to demonstrate the principles of physics, particularly projectile motion.
💡Marshmallow Catapults
Marshmallow Catapults is the name of the website where the Nerd-A-Pult can be purchased. It indicates the original purpose of the device, which is to launch marshmallows, but in the video, it is repurposed for educational purposes to demonstrate physics concepts.
💡Trigonometry
Trigonometry is a branch of mathematics that deals with the relationships between the angles and sides of triangles. In the video, trigonometric functions (sine and cosine) are used to break down the initial velocity into its horizontal and vertical components, which are essential for analyzing the projectile motion of the ball.
💡Uniformly Accelerated Motion
Uniformly accelerated motion describes the motion of an object whose acceleration is constant. In the video, the ball's motion in the y-direction is an example of uniformly accelerated motion because the acceleration due to gravity is constant, allowing the use of specific equations to calculate the displacement.
💡Scalar
A scalar is a quantity that has magnitude but no direction. In the context of the video, the change in time calculated for the x-direction is a scalar because it does not have a directional component; it is the same regardless of the axis along which the motion occurs.
💡Equations of Motion
The equations of motion are mathematical formulas used to describe the motion of objects under various conditions. In the video, the equations of motion for constant velocity and uniformly accelerated motion are applied to analyze the horizontal and vertical components of the ball's trajectory.
💡Physics
Physics is the natural science that studies matter, its motion, and the forces that act on it. The video is an educational demonstration of physics principles, particularly projectile motion, using a practical experiment with the Nerd-A-Pult to launch a ball and predict its trajectory.
Highlights

Introduction of the Nerd-A-Pult and its use for an Introductory Projectile Motion Problem

Source of the Nerd-A-Pult and its original purpose of launching marshmallows

Retrofitting the Nerd-A-Pult with a ball instead of marshmallows

Problem statement: Launching a ball with specific initial speed and angle to land in a basket

Understanding the horizontal displacement and the goal of finding the vertical displacement

Breaking down the initial velocity into its x and y components

Calculation of the initial velocity in the y-direction using sine of the angle

Calculation of the initial velocity in the x-direction using cosine of the angle

Decision to solve for change in time using the x-direction due to having two known variables

Determination of change in time using the x-direction's velocity and displacement

Use of change in time, a scalar, to solve for displacement in the y-direction

Application of uniformly accelerated motion equations to find the y-displacement

Conclusion that the basket should be placed 6.0 centimeters below the launch point

Demonstration of the solution's practical application with an outdoor test

Successful landing of the ball in the basket, confirming the accuracy of the calculations

Quick review summarizing the steps taken to solve the projectile motion problem

Transcripts

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