Final answer:
The impact speed of the cannon ball can be calculated by resolving the initial velocity into horizontal and vertical components, using kinematic equations to find the final velocity components, and then combining them with the Pythagorean theorem.
Step-by-step explanation:
Determining the Cannon Ball's Impact Speed
The question involves finding the impact speed of a cannon ball that is fired at an angle with a given initial velocity from an elevated position, which is a common problem in physics related to projectile motion and kinematics.
Breakdown of the Steps to Solve the Problem
- Resolve the initial velocity into horizontal and vertical components using trigonometric functions.
- Use the kinematic equations to calculate the final vertical velocity considering the gravitational acceleration and the initial height of the projectile.
- Since there is no air resistance, the horizontal velocity remains constant.
- Combine the final horizontal and vertical velocities to determine the impact speed using the Pythagorean theorem.
To solve the problem, first determine the horizontal (Vx) and vertical (Vy) components of the initial velocity. Vx is given by 82.0 m/s * cos(35.0°) and Vy is given by 82.0 m/s * sin(35.0°). The horizontal velocity will not change because there is no air resistance, but the vertical velocity will change due to gravity.
Use the kinematic equation Vy_final = Vy_initial + at to find the final vertical velocity. The time of flight (t) can be found using the kinematic equation that includes initial vertical velocity, gravitational acceleration, and displacement. Once t is determined, use it to calculate the final vertical velocity. Then use the Pythagorean theorem to find the combined final impact velocity (V_impact = √(Vx^2 + Vy_final^2)).
These calculations are based on the principles of projectile motion — an important topic in the study of kinematics in physics.