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A sphere rolls down an elevated track and becomes airborne. Height-1: h1 = 0.32 m Height-2: h2 = 1.14 m What is the Launch Velocity of the ball when it leaves the track and goes airborne?

A sphere rolls down an elevated track and becomes airborne. Height-1: h1 = 0.32 m Height-2: h2 = 1.14 m What is the Launch Velocity of the ball when it leaves the track and goes airborne?

College Physics
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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A sphere rolls down an elevated track and becomes airborne.

Height-1: h1 = 0.32 m

Height-2: h2 = 1.14 m


What is the Launch Velocity of the ball when it leaves the track and goes airborne?

### Section: Projectile Motion - Educational Resource #### Title: Analyzing the Launch Velocity of a Sphere in Projectile Motion **Introduction:** Projectile motion is a common phenomenon in physics that describes the motion of objects launched into the air and influenced by gravity. In this example, we study the motion of a sphere rolling down an elevated track until it becomes airborne. **Illustration:** The provided diagram shows a sphere that rolls down a sloped, elevated track and subsequently becomes airborne. The path of the sphere after it leaves the track follows a parabolic trajectory due to the influence of gravity. **Key Parameters and Analysis:** 1. **Diagram Explanation:** - The sphere starts at height \( h_1 \). - After rolling down the track, it launches into the air and falls to the ground at height \( h_2 \). - The horizontal distance covered by the sphere from the launch point to the landing point is referred to as the "Range." 2. **Heights:** - **Height-1 (\( h_1 \))**: This is the height from which the sphere starts rolling down the track. \( h_1 = 0.32 \) meters. - **Height-2 (\( h_2 \))**: This is the height from which the sphere is airborne to where it lands on the ground. \( h_2 = 1.14 \) meters. **Problem Statement:** What is the launch velocity of the sphere when it leaves the track and becomes airborne? **Solution Approach:** To calculate the launch velocity of the sphere, we can use principles from the physics of projectile motion. This involves: 1. **Determining the Time of Flight:** Using the vertical motion equations to find the time \( t \) it takes for the sphere to fall from \( h_1 \) to \( h_2 \). 2. **Determining the Horizontal Range:** Using the provided range to determine the horizontal displacement covered during the time of flight. 3. **Calculating Launch Velocity:** Combining these equations to solve for the launch velocity with considerations of horizontal and vertical components. For an educational resource, the detailed steps and formulae will follow, showing the derivation of the launch velocity. This requires solving simultaneous equations that relate the vertical descent due to gravity and horizontal motion. **Conclusion:** Understanding how to determine the launch velocity of an object in projectile motion
Transcribed Image Text:### Section: Projectile Motion - Educational Resource #### Title: Analyzing the Launch Velocity of a Sphere in Projectile Motion **Introduction:** Projectile motion is a common phenomenon in physics that describes the motion of objects launched into the air and influenced by gravity. In this example, we study the motion of a sphere rolling down an elevated track until it becomes airborne. **Illustration:** The provided diagram shows a sphere that rolls down a sloped, elevated track and subsequently becomes airborne. The path of the sphere after it leaves the track follows a parabolic trajectory due to the influence of gravity. **Key Parameters and Analysis:** 1. **Diagram Explanation:** - The sphere starts at height \( h_1 \). - After rolling down the track, it launches into the air and falls to the ground at height \( h_2 \). - The horizontal distance covered by the sphere from the launch point to the landing point is referred to as the "Range." 2. **Heights:** - **Height-1 (\( h_1 \))**: This is the height from which the sphere starts rolling down the track. \( h_1 = 0.32 \) meters. - **Height-2 (\( h_2 \))**: This is the height from which the sphere is airborne to where it lands on the ground. \( h_2 = 1.14 \) meters. **Problem Statement:** What is the launch velocity of the sphere when it leaves the track and becomes airborne? **Solution Approach:** To calculate the launch velocity of the sphere, we can use principles from the physics of projectile motion. This involves: 1. **Determining the Time of Flight:** Using the vertical motion equations to find the time \( t \) it takes for the sphere to fall from \( h_1 \) to \( h_2 \). 2. **Determining the Horizontal Range:** Using the provided range to determine the horizontal displacement covered during the time of flight. 3. **Calculating Launch Velocity:** Combining these equations to solve for the launch velocity with considerations of horizontal and vertical components. For an educational resource, the detailed steps and formulae will follow, showing the derivation of the launch velocity. This requires solving simultaneous equations that relate the vertical descent due to gravity and horizontal motion. **Conclusion:** Understanding how to determine the launch velocity of an object in projectile motion
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