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 two-line road, or two one-dimensional projectiles traveling in the same or opposite directions while moving through the air.

 spursuer = "gap" + sleader vot + ½at2 number vot + ½at2 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 side-by-side) 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 4-year old son a 10-second head-start. The pool is 25-meters 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 s-t 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 "one-way" 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/sec2. 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.

 spursuer = "gap" + sleader vot + ½at2 number vot + ½at2 vt vt s > 0 s < 0 18t + ½(-1)t2 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 s-t 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 v-t graph for this problem.