Resource Lesson
Chase Problems
Printer Friendly Version
In many problems, two objects are either approaching each other, chasing each other, or trying to get away from each other. Some examples might be: a police car chasing a speeding car, a passenger chasing a departing train or bus, an ambulance moving through traffic, two cars moving through an intersection, two vehicles coming towards each other on a twoline road, or two onedimensional projectiles traveling in the same or opposite directions while moving through the air.
s
_{pursuer}
= "gap" + s
_{leader}
v
_{o}
t + ½at
^{2}
number
v
_{o}
t + ½at
^{2}
vt
vt
Each column in the above table states the allowed behaviors for the pursuer and the leader. Each participant can either be experiencing accelerated or linear motion. The numerical value of the "gap" can be equal to zero (if the two objects start sidebyside) or it can be a nonzero number. The parameter
t
, for time, unites the equations. To solve chase equations, you first determine the time that is required for the two objects to come together  then, you use that time to determine the position of their collision.
To work this type of problem, one object is considered the leader and the other is the pursuer. The pursuer, in reaching the leader's final location, must not only close the leader's original gap but also account for any subsequent displacement the leader travels while being chased.
In the first example,
Refer to the following information for the next six questions.
In a swimming race, a father gives his 4year old son a 10second headstart. The pool is 25meters long. The child swims at 0.80 m/sec while the father swims at 1.20 m/sec.
How far is the child ahead of the father when the father gets to start swimming?
What chase equation must you solve to determine the winner?
At what time does the father come up alongside his son?
How far has the father swum at that point?
Who wins the race?
Describe the st graph for this problem.
In this next example, one object will maintain a constant velocity while the second will experience a negative acceleration in an attempt to avoid a collision.
Refer to the following information for the next ten questions.
Inadvertently, a car is driving at 13 m/sec the wrong direction down a "oneway" road as she searches for a store's address, oblivious to other traffic on the road. Coming from the opposite direction is a delivery truck that is moving at 18 m/sec. The car and truck are 500 meters apart when the truck driver applies his brakes, resulting in an acceleration of

1 m/sec
^{2}
. Once the truck driver brings his truck to a stop, he will remain at rest for the remainder of the problem.
To work this problem, we will consider the truck the pursuer and the car the leader.
s
_{pursuer}
= "gap" + s
_{leader}
v
_{o}
t + ½at
^{2}
number
v
_{o}
t + ½at
^{2}
vt
vt
s > 0
s < 0
18t + ½(1)t
^{2}
500 meters
13t
Using the information in the chart, what initial equation should we use to solve for
t
?
Based on your equation, what values of
t
are possible solutions to our problem?
How far the truck travel while coming to a stop?
How much time did the truck require to come to a stop?
How far did the car continue to travel forward while the truck was stopping?
When the truck first came to a complete stop how far away was the oncoming car?
How much time did the car require to travel the remaining distance to crash into the stopped truck?
Describe the st graph for this problem.
How much total time passed between when the truck first saw the car coming the wrong direction down the alley and the two vehicles collided?
Describe the vt graph for this problem.
Related Documents
Lab:
Labs 
A Photoelectric Effect Analogy
Labs 
Acceleration Down an Inclined Plane
Labs 
Ballistic Pendulum: Muzzle Velocity
Labs 
Coefficient of Friction
Labs 
Coefficient of Kinetic Friction (pulley, incline, block)
Labs 
Collision Pendulum: Muzzle Velocity
Labs 
Conservation of Momentum
Labs 
Cookie Sale Problem
Labs 
Flow Rates
Labs 
Freefall MiniLab: Reaction Times
Labs 
Freefall: Timing a Bouncing Ball
Labs 
Galileo Ramps
Labs 
Gravitational Field Strength
Labs 
Home to School
Labs 
InterState Map
Labs 
LAB: Ramps  Accelerated Motion
Labs 
LabPro: Newton's 2nd Law
Labs 
LabPro: Uniformly Accelerated Motion
Labs 
Mass of a Rolling Cart
Labs 
Moment of Inertia of a Bicycle Wheel
Labs 
Monkey and the Hunter Animation
Labs 
Monkey and the Hunter Screen Captures
Labs 
Projectiles Released at an Angle
Labs 
Ramps: Sliding vs Rolling
Labs 
Range of a Projectile
Labs 
Roller Coaster, Projectile Motion, and Energy
Labs 
Rube Goldberg Challenge
Labs 
Target Lab: Ball Bearing Rolling Down an Inclined Plane
Labs 
Terminal Velocity
Labs 
Video LAB: A Gravitron
Labs 
Video Lab: Ball Bouncing Across a Stage
Labs 
Video LAB: Ball ReBounding From a Wall
Labs 
Video Lab: Cart Push #2 and #3
Labs 
Video Lab: Falling Coffee Filters
Labs 
Video Lab: TwoDimensional Projectile Motion
Resource Lesson:
RL 
Accelerated Motion: A Data Analysis Approach
RL 
Accelerated Motion: VelocityTime Graphs
RL 
Analyzing SVA Graph Combinations
RL 
Average Velocity  A Calculus Approach
RL 
Chase Problems: Projectiles
RL 
Comparing Constant Velocity Graphs of PositionTime & VelocityTime
RL 
Constant Velocity: PositionTime Graphs
RL 
Constant Velocity: VelocityTime Graphs
RL 
Derivation of the Kinematics Equations for Uniformly Accelerated Motion
RL 
Derivatives: Instantaneous vs Average Velocities
RL 
Directions: Flash Cards
RL 
Freefall: Horizontally Released Projectiles (2DMotion)
RL 
Freefall: Projectiles in 1Dimension
RL 
Freefall: Projectiles Released at an Angle (2DMotion)
RL 
Monkey and the Hunter
RL 
Summary: Graph Shapes for Constant Velocity
RL 
Summary: Graph Shapes for Uniformly Accelerated Motion
RL 
SVA: Slopes and Area Relationships
RL 
Vector Resultants: Average Velocity
Review:
REV 
Test #1: APC Review Sheet
Worksheet:
APP 
Hackensack
APP 
The Baseball Game
APP 
The Big Mac
APP 
The Cemetary
APP 
The Golf Game
APP 
The Spring Phling
CP 
2D Projectiles
CP 
Dropped From Rest
CP 
Freefall
CP 
NonAccelerated and Accelerated Motion
CP 
Tossed Ball
CP 
Up and Down
NT 
Average Speed
NT 
BackandForth
NT 
Crosswinds
NT 
Headwinds
NT 
Monkey Shooter
NT 
Pendulum
NT 
Projectile
WS 
Accelerated Motion: Analyzing VelocityTime Graphs
WS 
Accelerated Motion: Graph Shape Patterns
WS 
Accelerated Motion: Practice with Data Analysis
WS 
Advanced Properties of Freely Falling Bodies #1
WS 
Advanced Properties of Freely Falling Bodies #2
WS 
Advanced Properties of Freely Falling Bodies #3
WS 
Average Speed and Average Velocity
WS 
Average Speed Drill
WS 
Charged Projectiles in Uniform Electric Fields
WS 
Chase Problems #1
WS 
Chase Problems #2
WS 
Chase Problems: Projectiles
WS 
Combining Kinematics and Dynamics
WS 
Constant Velocity: Converting Position and Velocity Graphs
WS 
Constant Velocity: PositionTime Graphs #1
WS 
Constant Velocity: PositionTime Graphs #2
WS 
Constant Velocity: PositionTime Graphs #3
WS 
Constant Velocity: VelocityTime Graphs #1
WS 
Constant Velocity: VelocityTime Graphs #2
WS 
Constant Velocity: VelocityTime Graphs #3
WS 
Converting st and vt Graphs
WS 
Energy Methods: More Practice with Projectiles
WS 
Energy Methods: Projectiles
WS 
Force vs Displacement Graphs
WS 
Freefall #1
WS 
Freefall #2
WS 
Freefall #3
WS 
Freefall #3 (Honors)
WS 
Horizontally Released Projectiles #1
WS 
Horizontally Released Projectiles #2
WS 
Kinematics Along With Work/Energy
WS 
Kinematics Equations #1
WS 
Kinematics Equations #2
WS 
Kinematics Equations #3: A Stop Light Story
WS 
Lab Discussion: Gravitational Field Strength and the Acceleration Due to Gravity
WS 
PositionTime Graph "Story" Combinations
WS 
Projectiles Released at an Angle
WS 
Rotational Kinetic Energy
WS 
SVA Relationships #1
WS 
SVA Relationships #2
WS 
SVA Relationships #3
WS 
SVA Relationships #4
WS 
SVA Relationships #5
WS 
Work and Energy Practice: An Assortment of Situations
TB 
2A: Introduction to Motion
TB 
2B: Average Speed and Average Velocity
TB 
Antiderivatives and Kinematics Functions
TB 
Honors: Average Speed/Velocity
TB 
Kinematics Derivatives
TB 
Projectile Summary
TB 
Projectile Summary
TB 
Projectiles Mixed (Vertical and Horizontal Release)
TB 
Projectiles Released at an Angle
TB 
Set 3A: Projectiles
PhysicsLAB
Copyright © 19972018
Catharine H. Colwell
All rights reserved.
Application Programmer
Mark Acton