College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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Using the diagram, apply conservation of energy in order to predict what the speed of the ball is when it reaches the end of the track. Form the expression symbolically
Transcribed Image Text:**Projectile Motion Analysis**
This diagram represents a scenario involving projectile motion in physics, often used to illustrate how objects move through space influenced by gravity. Below is a detailed description and explanation:
1. **Starting Point and Initial Conditions**:
- **Released from Rest**: The object starts from rest at a height \( h \) above the launching surface. Meaning it has an initial velocity of 0.
2. **Movement and Launch**:
- The object, attached to a string or pivot, swings down due to gravity.
- Upon reaching the end of its arc, it is **launched straight off** the edge of the surface with a horizontal velocity \( v \).
3. **Trajectory Path**:
- Once launched, the object follows a parabolic trajectory due to the combination of its horizontal velocity and the vertical pull of gravity.
- This path is divided into horizontal and vertical components.
4. **Horizontal Launch Velocity ( \( v \) )**:
- The launch is horizontal which means that at the point of launch, all velocity is in the horizontal direction. The horizontal velocity \( v \) remains constant throughout the flight in the absence of air resistance.
5. **Vertical Motion**:
- The vertical component of the motion starts from zero (since the launch is horizontal) and increases linearly with time due to gravity (\( g \)).
- \( y \) represents the vertical distance the object falls from the launch point.
6. **Displacement Upon Landing**:
- \( x \) depicts the horizontal distance traveled by the object from the launch point to the point where it impacts the ground.
- \( y \) corresponds to the total vertical distance fallen from the launch point down to the ground.
7. **Key Variables**:
- **\( h \)**: Initial height from which the object is released.
- **\( v \)**: Horizontal launch velocity of the object.
- **\( x \)**: Horizontal distance traveled after launch.
- **\( y \)**: Vertical distance traveled after launch, equivalent to \( h \) if the object falls directly from the edge.
Understanding this diagram helps in computing:
- **Projectile Range**: The horizontal distance \( x \) the object travels, calculated using the formula \( x = v \cdot t \), where \( t \) is the time of flight.
- **Time of Flight**: The total time the object
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