To determine the angle of elevation of a cannon when the bullet reaches a distance of 220 meters with an initial velocity of 50 m/s, you can use the following steps:
1. Understand the projectile motion: When an object is launched into the air, it follows a curved path known as projectile motion under the influence of gravity.
2. Break down the motion into horizontal and vertical components: The initial velocity of 50 m/s can be separated into horizontal (Vx) and vertical (Vy) components. Vx remains constant, while Vy changes due to gravity.
3. Calculate the time of flight: The time it takes for the projectile to reach a horizontal distance of 220 meters can be calculated using the formula: time = distance / horizontal velocity.
4. Calculate the maximum height: Using the formula for vertical motion, you can find the maximum height the projectile reaches.
5. Determine the angle of elevation: Once you have the time of flight and the maximum height, you can calculate the angle of elevation using trigonometry. The angle θ can be found using the formula: tan(θ) = (maximum height) / (horizontal distance).
By following these steps and applying the formulas of projectile motion and trigonometry, you can determine the angle of elevation of the cannon needed to achieve a range of 220 meters with an initial velocity of 50 m/s.
