Purpose: Apply the concepts of two-dimensional kinematics (projectile motion) to predict the impact point of an object as its velocity increases.

Introduction: The most common example of an object that is moving in two dimensions is a projectile. A projectile is an object upon which the only force acting is gravity. That is to say a projectile is any object that once projected or dropped continues in motion by its own, and is influenced only by the downward force of gravity. There are a number of examples of projectiles, such as an object dropped from rest, an object that is thrown vertically upward, and an object which is thrown upward at an angle to the horizontal is also a projectile. Since a projectile is an object that only has a single force acting on it, the free-body diagram of a projectile would show only a single force acting downwards; labeled force of gravity. Regardless of which direction a projectile is moving, the free-body diagram of the projectile is still as depicted in the diagram at the right.

In the case of projectiles, one can use information about the initial velocity and position of a projectile to predict such things as how much time the projectile is in the air and how far the projectile will go. For example, a projectile launched with an initial horizontal velocity from an elevated position will follow a parabolic path to the ground. Unknowns include the initial speed of the projectile, the initial height of the projectile, the time of flight, and the horizontal distance of the projectile. These can all be solved for by using the following equations: [pic] and [pic]. Where y is vertical distance, x is horizontal distance, t is time, a is acceleration, and v is velocity.

Question: What happens to an object’s impact point in two-dimensional kinematics when its speed increases?

Hypothesis: If the speed of an object increases in two-dimensional kinematics then its impact point will also increase because the speed acquired in one dimension allows the object to travel further even when travelling in the second dimension.

Variables: Independent: SpeedIndependent: Impact Point

Controls: way of releasing object (ramp), weight/size of object, point of release on the ramp (in each trial), distance ball travels across the table, same table height.

Materials:Computerone photogateright angle clamp

Logger proballmasking tape

3 ramps of increasing sizering standmeter stick

Preliminary Questions: 1.What information is needed to predict how long an object reaches the floor when dropped from rest? 2. If an object is travelling at a known horizontal velocity, how can the distance it travels be calculated?

Answers to preliminary questions: 1. To determine the time it takes for an object to reach the floor when dropped from rest, you must know the height from which it was dropped, its acceleration (in this case is gravity: 9.8 m/s2), and its initial velocity (in this case is 0 m/s, because it began from rest). 2. The distance an object travels at a known horizontal velocity can be calculated by knowing the time it takes to reach its impact point.

Procedure: 1. Set up a low ramp on a table so that a ball may roll down it, across a short section of the table, and off the edge.

2. Position the photogate so that the ball rolls directly through the centre. Place it on the section of the table and not on the ramp.

3. Secure the photogate with a ring stand and right angle clamp. Make sure when the ball rolls through, it does not touch either side of the photogate.

4. Connect the photogate to the digital 1 port and connect the port to the computer.

5. Prepare the computer by opening up LoggerPro. Select the photogate, making sure it is unblocked, and set it to gate timing.

6. Measure the diameter of the ball you are using and input its value into the program.

7. Mark a spot on the ramp so that you can roll the...

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