Projectile Motion

By measuring the speed of a ball as it descended from a specific height we conducted an experiment to forecast projectile motion. The first thing we did was roll a ball down a series of ramps that were spaced at various heights. The initial velocity of the ball was then calculated using a pair of photogates shortly before it rolled off the ramp's surface and landed on the ground. The horizontal separation from the surface where the ball landed was also measured. We were able to create a graphical model to illustrate the relationship between surface height and horizontal landing distance using the information at our disposal. We could, therefore, predict the specific location where a ball could fall from any other unspecified height. Through this experiment, we learned the different ways of predicting the horizontal landing distance of a projectile.

Experiment: Projectile Motion

Introduction and Data Collection

Introduction: This experiment will involve rolling down a ball on various ramps that have been positioned at different heights. It aims at developing an experimental method that can test a hypothesis about projectile motion. Two primary methods can be used to test the hypothesis. The first approach is through creating a model to predict where a projectile will fall from a known height. Secondly, we make use of various kinematic equations. The two primary equations that that can help in determining the distance from the edge of the table that the ball will land are; Y=Voyt+1/2ayt2 and X=Voxt+1/2axt2. Whereby Y is the table height measured during experimentation, Vox and Voy are the initial velocities, ax is the horizontal acceleration and ay the vertical acceleration. Alternatively, one can use both potential and kinetic energy equations to determine the time taken for the ball to hit the floor. That is; Pe=mgh and Ke=1/2mv2, where m is the mass of the ball, g is the gravity and, h the height.

Hypothesis

The data collected can be used to predict the probable position that the ball will land if it falls from a much higher height.

Methods

We use a pair of photogates to determine the initial velocity as the ball transits from one ramp to the other. This photogate produces infrared light which can be detected whenever the falling ball blocks the beam. However, it is important to take note of the distance between the photogates and the direction of the ball in order to determine the velocity. We also measure the horizontal distance from the point where the ball hits the floor. Using this information, we then create a graphical model to show the relationship between surface height and horizontal landing distance. Other equipment used during the experiment include; metal balls, projectile ramp, tape measure, plumb bob and two ring stands.

Results

The initial height of the projectile before leaving the tables was measured as 0.883 meters. This figure was obtained by taking the ramp and the ball to the test station such that the ball will roll between the photogates before falling. The distance between the gates was set to be approximately 0.022m

After inputting the data in the loggerpro computer simulation tool, we were able to generate the graphs shown below.

Analysis

After taking the average of the velocities measures using the photogates, we also determine the minimum and maximum initial velocities as shown below;

The experiment has taught us two different ways of predicting the horizontal landing distance of a projectile. The first approach involves creating a model about how the ball behaves from various heights while the second one involves combining kinematic equations into a single expression. However, I prefer the model approach because it allows one to take various measures and then get the average which in my view is more accurate compared to using the equations. Nevertheless, the two methods gave almost similar predictions.

Conclusion

The experiment has made us learn how to predict the horizontal landing distance of a projectile. It involved running a ball through craves located at different positions. As it falls from the various heights, a pair of photogates was used to determine its velocity. The gate emits an infrared beam whose transmission can be blocked by a passing ball.