🔖 Topics

  • Kinematics Equations
  • Breaking Down a Kinematics Problem of Two Dimensions

🎯 Objectives

  • Break down the two-dimensional motion of an object into its position, velocity, and acceleration.
  • Relate the different dimensions of motion using time.
  • Calculate the properties of an object moving under a constant acceleration.

📋 Sequence

  • Kinematics practice in two dimensions
    • Draw a free-body diagram
    • Draw a coordinate axis
    • Break up the problem by dimension
    • List known values
    • Determine useful kinematics equations
    • Solve for unknowns

🖥️ Animations, Simulations, Activities

N/A

📝 Practice Problems

Firing an Arrow: An arrow is shot from a bow and arrow with an initial speed v = 10 m/s at an angle of \(30^\circ\) above the ground.

  • What is the time of flight?
  • What is the horizontal distance covered?
  • What is the maximum height?
  • What is the angle at which it hits the ground?

Throwing a Ball Off a Cliff: A ball is thrown with an initial speed v = 10 m/s at an angle of \(30^\circ\) off a cliff that is 20 meters above the ground.

  • What is the time of flight?
  • What is the horizontal distance covered?
  • What is the maximum height?
  • What is the angle at which it hits the ground?

Projectile Fired From a Cannon: A cannonball is fired from a cannon located and flies in an arc towards a target that is 75 meters away. After five seconds of flight, it hits the target.

  • What is the maximum height?
  • What is the initial velocity of the launch?
  • What is the angle of launch?
  • What is the angle at which it hits the ground?

✅ Partial Solutions

N/A

📘 Connected Resources

  • Giambattista, Alan, et al. College Physics With an Integrated Approach to Forces and Kinematics. 5th ed., McGraw-Hill Education, 2020.