Objectives

1. Determine the launch velocity of a spring launcher by analyzing a projectile’s motion.
2. Predict the projectile’s landing point when it is launched at a different angle.
3. Test your prediction’s accuracy by performing multiple launches.

Resources/Guides

• Mobile phone, digital camera, or other device for taking video
• Tracker Software
  • Quick Tutorial on Tracker
  • Video: Getting Started with Tracker
• Projectile launcher
• Cardboard backdrop
• Meter stick

Background

Projectile motion is the simplest non-trivial form of an object in two-dimensional motion. Trivial would be an object moving at constant velocity – it travels in a straight line, so you could just pick your x-axis to be in the direction of motion and analyze as motion in one dimension. In projectile motion, there is a constant acceleration (usually assumed to be the downward acceleration of gravity), so you have to analyze the motion two-dimensionally.

In general, projectile motion describes an object given an initial velocity v_0 at an angle \theta from the horizontal. If air resistance is neglected, the only acceleration is in the y-direction due to gravity, so the x– and y-position of the projectile at time t, for example, are given by the kinematic equations for motion with constant acceleration.

x=x_0+v_0 t \cos \theta y=y_0+v_0 t \sin \theta - \tfrac{1}{2}gt^2

Setup

Load a projectile into the spring launcher and use a plunger to push the ball down until the spring launcher clicks once. Pushing the projectile in farther will launch it too far to capture the motion on video easily. Tilt the launcher at a 45 degree angle and record a video while the projectile is launched.

Guideposts/Hints

• You obviously want to hold your camera steady or mount it on a tripod when making a video to analyze the motion of your projectile. You also want to make sure your camera is pointed perpendicular to the plane of the projectile’s motion. What happens to the projectile’s apparent velocity in the video if it is traveling partially toward or away from the camera?
• If you are using the lab’s Casio Exilim digital cameras, you may find this helpful: Fast Shutter Mode for Motion Capture with Casio Exilim Camera