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### 307-L: Cannon Problems 1: Concepts and Numeric Analysis

• Topic Cluster: Kinematics
• Topic: Projectile Motion
• Objective: Conceptually explain the motion in each dimension of an object launched at an angle; use this information to solve for relevant numeric quantities.
• Content: An object fired at an angle moves forward with a constant velocity in the horizontal dimension and moves identically to an object thrown directly upward in the vertical dimension.
• Level: 4

#### BACK to Ladder Projectile Motion

This pod will deal with cannons that fire a shot that lands on exactly the same level. The problems bring together the concepts of the pop-up and horizontal launch problems, and they are among the most classic physics problems!

#### Basic cannon Problem

1. A cannon is aimed at an angle of 30 degrees. It fires a cannonball with a speed of 20 m/s. The cannonball rises and falls and then lands at precisely the vertical level it was fired at.
1. First, break the initial velocity of the cannonball into horizontal and vertical components using this method.
2. Similarly to a horizontal launch problem, we will break the motion into two components. In the horizontal dimension, the object moves at a constant speed forward. In the vertical dimension, the object is initially moving upward and then falls downward to the same point, similarly to a pop-up problem. Fill out the table below, which describes the quantities involved in this problem:
3. Determine the total time that the cannonball is in the air.
4. Determine the range of the cannonball, that is, the horizontal displacement of the cannonball before it strikes the ground.
2. We will repeat a similar question with different values. A cannon is aimed at an angle of 20 degrees. It fires a cannonball with a speed of 15 m/s. The cannonball falls to the same vertical position from where it was fired.
1. Break the initial velocity of the cannon into horizontal and vertical components.
2. Fill out the table below, which describes the quantities involved.
3. Determine the total time that the cannonball is in the air.
4. Determine the horizontal range of the cannonball.
3. A cannon is aimed at an angle of 85 degrees. It fires a cannonball with a speed of 40 m/s. The cannonball falls to the same vertical position from where it was fired.
1. Break the initial velocity of the cannon into horizontal and vertical components.
2. Fill out the table below, which describes the quantities involved.
3. Determine the total time that the cannonball is in the air.
4. Determine the horizontal range of the cannonball.

Use $$g = 9.81 \frac{\text{m}}{\text{s}^2}$$Answer the following questions to three significant figures of accuracy.

1. A cannon is at an angle of 45.0 degrees above the horizontal and fires a shot with an initial velocity of 20.0 m/s. If the cannonball lands on the same level it was fired at, determine the horizontal range of the cannonball.
2. A cannon is at an angle of 35.0 degrees above the horizontal and fires a shot with an initial velocity of 28.0 m/s. If the cannonball lands on the same level it was fired at, determine the horizontal range of the cannonball.
3. A cannon is at an angle of 65.0 degrees above the horizontal and fires a shot with an initial velocity of 10.0 m/s. If the cannonball lands on the same level it was fired at, determine the horizontal range of the cannonball.