The Ballistic Pendulum

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In this physics crime lab or demonstration, learners pretend they are criminologists and must find the "muzzle velocity" (speed of the bullet as it leaves the gun) of a gun used to commit a crime. Learners build an apparatus to fire a dart from a plastic toy gun into the open end of a cut-off plastic water bottle which has been stuffed with a plastic bag and suspended as a pendulum. Knowing the mass of the dart, the mass of the water bottle-bag combination, and the vertical rise of the water-bottle bag combination with the dart in it, simple energy and momentum considerations are used to find the muzzle velocity of the dart.

Quick Guide

Preparation Time:
10 to 30 minutes

Learning Time:
1 to 2 hours

Estimated Materials Cost:
Over $20 per group of students

Age Range:
Ages 14 - 18

Resource Types:
Activity, Demonstration, Experiment/Lab Activity


Materials List (per group of students)

  • toy dart gun with suction cup darts
  • balane
  • 1 PVC 1/2 in. pipe, 12 in. long
  • 5 PVC 1/2 in. pipe, 4 in. long
  • 2 PVC 1/2 in. pipe, 2 in. long
  • 3 PVC 1/2 in. 90 degree elbows
  • 2 PVC 1/2 in. T's
  • plastic water bottle, 500 mL, with top
  • plastic grocery bag
  • string
  • tape, translucent and/or masking
  • jumbo paper clip
  • 5x8 index card
  • washer, steel, 3/4 in (approximate mass 50 g)
  • marker pen
  • ruler
  • scissors and/or utility knife
  • calculator


  • Mathematics
    • Algebra
      • Equations and Inequalities
      • Variables and Expressions
    • Data Analysis and Probability
      • Data Analysis
      • Data Collection
    • Measurement
    • Number and Operations
  • Physical Sciences
    • Energy
      • Potential and Kinetic Energy
    • Motion and Forces
      • Momentum and Velocity
      • Projectile Motion
    • Structure and Properties of Matter
      • Mass and Weight
  • The Nature of Science
    • The Scientific Process
      • Conducting Investigations
      • Gathering Data
      • Formulating Explanations
      • Communicating Results
    • Science as a Career

Informal Categories

  • Crime Science


To use this activity, learners need to:

  • see
  • read
  • touch

Learning styles supported:

  • Involves hands-on or lab activities


This resource is part of:

Access Rights:

  • Free access


  • Rathjen, Don


  • All rights reserved, Exploratorium, 2008