D Two cannons aimed directly at each other fire simultaneously. The cannon balls have the same speed immediately after being fired. Some time later, the cannon balls collide at point P. O e increases as H decreases Oxe does not depend on H H How does xe, the horizontal distance from the edge of the building to where the cannon balls collide, depend on the height of the building H? Oxe decreases as H decreases

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ISBN:9781305952300
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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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**Projectile Motion: A Collision Experiment**

**Description of Experiment:**

Two cannons are aimed directly at each other and fire simultaneously. The cannonballs have the same speed immediately after being fired. At some point, the cannonballs collide at point \( P \).

**Diagrams and Variables:**

- **Gravity (\( g \)):** Acts downward on both projectiles.
- **Initial Speed (\( v_0 \)):** Both cannonballs have the same initial speed.
- **Point of Collision (\( P \)):** The location where the two projectiles meet.
- **Horizontal Distance (\( x_c \)):** The distance from the edge of a building to the collision point.
- **Total Horizontal Distance (\( D \)):** The full horizontal distance between the two cannons.
- **Building Height (\( H \)):** Height of the structure involved in the experiment.

**Question:**

How does \( x_c \), the horizontal distance from the edge of the building to where the cannonballs collide, depend on the height of the building \( H \)?

**Options:**
- \( x_c \) increases as \( H \) decreases
- \( x_c \) does not depend on \( H \)
- \( x_c \) decreases as \( H \) decreases

**Correct Answer:**
- \( x_c \) decreases as \( H \) decreases

This illustrates the relationship between horizontal distance and the height of the building, showcasing the principles of projectile motion in physics.
Transcribed Image Text:**Projectile Motion: A Collision Experiment** **Description of Experiment:** Two cannons are aimed directly at each other and fire simultaneously. The cannonballs have the same speed immediately after being fired. At some point, the cannonballs collide at point \( P \). **Diagrams and Variables:** - **Gravity (\( g \)):** Acts downward on both projectiles. - **Initial Speed (\( v_0 \)):** Both cannonballs have the same initial speed. - **Point of Collision (\( P \)):** The location where the two projectiles meet. - **Horizontal Distance (\( x_c \)):** The distance from the edge of a building to the collision point. - **Total Horizontal Distance (\( D \)):** The full horizontal distance between the two cannons. - **Building Height (\( H \)):** Height of the structure involved in the experiment. **Question:** How does \( x_c \), the horizontal distance from the edge of the building to where the cannonballs collide, depend on the height of the building \( H \)? **Options:** - \( x_c \) increases as \( H \) decreases - \( x_c \) does not depend on \( H \) - \( x_c \) decreases as \( H \) decreases **Correct Answer:** - \( x_c \) decreases as \( H \) decreases This illustrates the relationship between horizontal distance and the height of the building, showcasing the principles of projectile motion in physics.
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