### Projectile Motion: Sphere Rolling Down an Elevated Track#### Problem StatementA sphere rolls down an elevated track and becomes airborne. The diagram illustrates the path of the sphere from the point it leaves the track (height \( h_1 \)) to where it lands (height \( h_2 \)). The range of travel is the horizontal distance the sphere covers while airborne.#### Given Data- Height-1 (\( h_1 \)): 0.32 m- Height-2 (\( h_2 \)): 1.14 m#### ObjectiveDetermine the range of travel (distance) for the ball after it has launched from the track. Provide your answer in meters.##### Diagram ExplanationIn the provided diagram:- The left vertical section represents the initial height \( h_1 \), where the sphere is rolling off the track.- The projectile path is shown with a dashed parabola, depicting the sphere's trajectory as it travels towards the ground.- The right vertical section represents the final height \( h_2 \), where the sphere lands.- The horizontal distance between the initial and final heights is labeled “Range”, which is the value to be determined.#### TaskUsing the provided heights \( h_1 \) and \( h_2 \), calculate the horizontal distance the sphere travels after being launched from the track. Apply principles from projectile motion to solve this problem, considering factors such as initial velocity, acceleration due to gravity, and time of flight.#### ConclusionUpon finding the range, submit your answer in meters.---This problem helps in understanding projectile motion, an important concept in physics that deals with the trajectory of objects under the influence of gravity. It combines elements of kinematics and dynamics, offering practical insight into how objects move through space.

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Asphere rolls down an elevated track and becomes airborne. 71 Range Height-1: h1 = 0.32 m Height-2: h2= 1.14 m h₂ What is the Range of travel for the ball (Distance) after it has launched from the track? Give your answers in meters.

Asphere rolls down an elevated track and becomes airborne. 71 Range Height-1: h1 = 0.32 m Height-2: h2= 1.14 m h₂ What is the Range of travel for the ball (Distance) after it has launched from the track? Give your answers in meters.

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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Question

### Projectile Motion: Sphere Rolling Down an Elevated Track

#### Problem Statement
A sphere rolls down an elevated track and becomes airborne.

The diagram illustrates the path of the sphere from the point it leaves the track (height \( h_1 \)) to where it lands (height \( h_2 \)). The range of travel is the horizontal distance the sphere covers while airborne.

#### Given Data
- Height-1 (\( h_1 \)): 0.32 m
- Height-2 (\( h_2 \)): 1.14 m

#### Objective
Determine the range of travel (distance) for the ball after it has launched from the track. Provide your answer in meters.

##### Diagram Explanation
In the provided diagram:
- The left vertical section represents the initial height \( h_1 \), where the sphere is rolling off the track.
- The projectile path is shown with a dashed parabola, depicting the sphere's trajectory as it travels towards the ground.
- The right vertical section represents the final height \( h_2 \), where the sphere lands.
- The horizontal distance between the initial and final heights is labeled “Range”, which is the value to be determined.

#### Task
Using the provided heights \( h_1 \) and \( h_2 \), calculate the horizontal distance the sphere travels after being launched from the track. Apply principles from projectile motion to solve this problem, considering factors such as initial velocity, acceleration due to gravity, and time of flight.

#### Conclusion
Upon finding the range, submit your answer in meters.

---

This problem helps in understanding projectile motion, an important concept in physics that deals with the trajectory of objects under the influence of gravity. It combines elements of kinematics and dynamics, offering practical insight into how objects move through space.

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