How Do You Calculate the Launch Angle and Velocity of a Cannonball?

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In summary, the conversation discusses how to approach a physics problem involving a cannon shooting a ball and clearing a wall. The goal is to find the allowable launch angle and velocity, assuming gravity is 9.81 meters per second squared. The conversation suggests listing the equations for a projectile and using them to calculate the maximum height and find the range. Finally, the conversation mentions using the given range and height to create two equations for angle and speed.
  • #1
wisper
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Ok, I am having a hard time understanding how to approach this problem the correct way interms of physics.

A cannon shoots a ball going a total distance of 79.5 meters, clearing a wall 67.5 meters away from where it was initially shot. The wall is 17.58 meters high, what is the allowable launch angle and velocity? Assume gravity is 9.81 meters per second squared.
 
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  • #2
canon

draw the projectile
list all the equations of a projectile
try to calculate the maximum heigt
try to find range
 
  • #3
Write down the formulas for distance and height of a projectile depending on angle and initial speed. You know that the range (distance until the height is 0 again) is 79.5 and that the height 67.5 meters away is at least 17.58 meters. That gives you two equations for angle and speed.
 

1. What is a canon problem in kinematics?

A canon problem in kinematics refers to a type of physics problem that involves analyzing the motion of a projectile, such as a cannonball, as it travels through the air. This type of problem typically involves determining the initial velocity, position, and acceleration of the projectile, as well as its trajectory and other related factors.

2. How do you solve a canon problem in kinematics?

To solve a canon problem in kinematics, you will need to use the equations of motion, also known as the kinematic equations, which describe the relationships between the initial velocity, final velocity, acceleration, displacement, and time of a moving object. By plugging in the known values and solving for the unknowns, you can determine the various parameters of the projectile's motion.

3. What are the key concepts involved in solving a canon problem in kinematics?

The key concepts involved in solving a canon problem in kinematics include projectile motion, which describes the motion of an object in a curved path under the influence of gravity, as well as the kinematic equations mentioned earlier. Other important concepts include vector components, which are used to break down the initial velocity of the projectile into its horizontal and vertical components, and the principle of independence of motion, which states that the horizontal and vertical components of motion can be analyzed separately.

4. What are some common mistakes when solving a canon problem in kinematics?

Some common mistakes when solving a canon problem in kinematics include forgetting to convert units, such as using meters instead of kilometers, and not properly identifying the initial and final positions and velocities of the projectile. It is also important to pay attention to the direction of the velocity and acceleration vectors, as well as the sign conventions used in the kinematic equations.

5. How can understanding canon problems in kinematics be useful?

Understanding canon problems in kinematics can be useful in a variety of fields, including physics, engineering, and sports. By being able to analyze the motion of projectiles, you can make predictions about their trajectories and optimize their performance. This knowledge can also be applied to other types of motion, such as the movement of vehicles or objects in free fall, making it a valuable skill for any scientist or engineer.

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