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One kind of slingshot consists of a pocket that holds a pebble and is whirled on a circle of radius r. The pebble is released from the circle at an angle θ, so that it will hit the target. The distance to the target from the center of the circle is d. (See the drawing, which is not to scale.) The circular path is parallel to the ground, and the target lies in the plane of the circle. The distance d is 5.19 times the radius r. Ignore the effects of gravity in pulling the stone downward after it is released and find the angle θ.

One kind of slingshot consists of a pocket that holds a pebble and is whirled on a circle of radius r. The pebble is released from the circle at an angle θ, so that it will hit the target. The distance to the target from the center of the circle is d. (See the drawing, which is not to scale.) The circular path is parallel to the ground, and the target lies in the plane of the circle. The distance d is 5.19 times the radius r. Ignore the effects of gravity in pulling the stone downward after it is released and find the angle θ.

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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One kind of slingshot consists of a pocket that holds a pebble and is whirled on a circle of radius r. The pebble is released from the circle at an angle θ, so that it will hit the target. The distance to the target from the center of the circle is d. (See the drawing, which is not to scale.) The circular path is parallel to the ground, and the target lies in the plane of the circle. The distance d is 5.19 times the radius r. Ignore the effects of gravity in pulling the stone downward after it is released and find the angle θ.

### Diagram Explanation: Trajectory of a Pebble In this diagram, we visualize the trajectory path of a pebble aimed at a target point. Here’s a detailed explanation of the components and their roles: 1. **Circle Description**: - The circle is indicated with a dashed red line and represents the path along which the pebble travels when launched. - The center of the circle is marked as point \( C \). 2. **Pebble's Position**: - The point labeled "Pebble" is shown on the circumference of the circle. - A radius \( r \) extends from the center \( C \) to the pebble's position on the circle. 3. **Target Position**: - There is a point labeled "Target" located outside the circle. - The distance from the center \( C \) to the target is marked as \( d \). 4. **Angles and Measurements**: - The angle between the radius \( r \) and the line connecting the center \( C \) to the target is labeled as \( \theta \). - An adjacent angle to \( \theta \) is labeled as \( 35^\circ \) which suggests a base angle in the calculations relevant to the scenario. 5. **Direction**: - A curved arrow is drawn alongside the circle, indicating the direction of pebble's movement along the circular path. ### Contextual Use This diagram can be used to illustrate concepts related to projectile motion, circular motion dynamics, and trigonometric calculations in physics or mathematics education. The setup helps to explore variables such as angles, radii, and distances when a projectile changes its trajectory from a circular path towards a linear one aimed at a particular target.
Transcribed Image Text:### Diagram Explanation: Trajectory of a Pebble In this diagram, we visualize the trajectory path of a pebble aimed at a target point. Here’s a detailed explanation of the components and their roles: 1. **Circle Description**: - The circle is indicated with a dashed red line and represents the path along which the pebble travels when launched. - The center of the circle is marked as point \( C \). 2. **Pebble's Position**: - The point labeled "Pebble" is shown on the circumference of the circle. - A radius \( r \) extends from the center \( C \) to the pebble's position on the circle. 3. **Target Position**: - There is a point labeled "Target" located outside the circle. - The distance from the center \( C \) to the target is marked as \( d \). 4. **Angles and Measurements**: - The angle between the radius \( r \) and the line connecting the center \( C \) to the target is labeled as \( \theta \). - An adjacent angle to \( \theta \) is labeled as \( 35^\circ \) which suggests a base angle in the calculations relevant to the scenario. 5. **Direction**: - A curved arrow is drawn alongside the circle, indicating the direction of pebble's movement along the circular path. ### Contextual Use This diagram can be used to illustrate concepts related to projectile motion, circular motion dynamics, and trigonometric calculations in physics or mathematics education. The setup helps to explore variables such as angles, radii, and distances when a projectile changes its trajectory from a circular path towards a linear one aimed at a particular target.
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