### Exercise: Projectile Motion of a CannonballYou are attempting to find the range of a cannon by shooting a cannonball at different angles. The cannon fires the ball with a velocity of 105 m/s and you are firing across a level field. You try angles of 30°, 45°, and 60°.#### Questions:a. **How long is the cannonball in the air for each of the three attempts?**b. **What is the maximum height for each of the cannonballs?**c. **How far does each travel in the horizontal direction?**### Explanation:To solve these questions, you need to apply the principles of projectile motion. Each point below explains the different aspects that need to be calculated:1. **Time of Flight (T):** - The total time the projectile remains in the air. - Formula: \( T = \frac{2 \cdot V_0 \cdot \sin(\theta)}{g} \) - \( V_0 \): Initial velocity (105 m/s) - \( \theta \): Angle of projection (30°, 45°, 60°) - \( g \): Acceleration due to gravity (9.81 m/s²)2. **Maximum Height (H):** - The peak vertical position reached by the projectile. - Formula: \( H = \frac{V_0^2 \cdot \sin^2(\theta)}{2 \cdot g} \)3. **Horizontal Range (R):** - The total horizontal distance covered by the projectile. - Formula: \( R = \frac{V_0^2 \cdot \sin(2\theta)}{g} \)#### Steps to solve:1. **Calculate the Time of Flight for each angle (30°, 45°, 60°).**2. **Determine the Maximum Height reached for each angle.**3. **Compute the Horizontal Range for each angle.**By solving these equations using the given data, you can derive the specific details for each angle of projection.

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You are attempting to find the range of a cannon by shooting a cannonball at different angles. The cannon fires the ball with a velocity of 105 and you are firing across a level field. You try angles of 30°, 45°, and 60°.

You are attempting to find the range of a cannon by shooting a cannonball at different angles. The cannon fires the ball with a velocity of 105 and you are firing across a level field. You try angles of 30°, 45°, and 60°.

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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Projectile Motion

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### Exercise: Projectile Motion of a Cannonball

You are attempting to find the range of a cannon by shooting a cannonball at different angles. The cannon fires the ball with a velocity of 105 m/s and you are firing across a level field. You try angles of 30°, 45°, and 60°.

#### Questions:

a. **How long is the cannonball in the air for each of the three attempts?**

b. **What is the maximum height for each of the cannonballs?**

c. **How far does each travel in the horizontal direction?**

### Explanation:

To solve these questions, you need to apply the principles of projectile motion. Each point below explains the different aspects that need to be calculated:

1. **Time of Flight (T):**
- The total time the projectile remains in the air.
- Formula: \( T = \frac{2 \cdot V_0 \cdot \sin(\theta)}{g} \)
- \( V_0 \): Initial velocity (105 m/s)
- \( \theta \): Angle of projection (30°, 45°, 60°)
- \( g \): Acceleration due to gravity (9.81 m/s²)

2. **Maximum Height (H):**
- The peak vertical position reached by the projectile.
- Formula: \( H = \frac{V_0^2 \cdot \sin^2(\theta)}{2 \cdot g} \)

3. **Horizontal Range (R):**
- The total horizontal distance covered by the projectile.
- Formula: \( R = \frac{V_0^2 \cdot \sin(2\theta)}{g} \)

#### Steps to solve:

1. **Calculate the Time of Flight for each angle (30°, 45°, 60°).**
2. **Determine the Maximum Height reached for each angle.**
3. **Compute the Horizontal Range for each angle.**

By solving these equations using the given data, you can derive the specific details for each angle of projection.

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