15-Sept-2014: Trajectories and Projectile Motion

The purpose of this lab was to use the understanding of projectile motion to predict the impact point of a ball on an inclined plane.

The apparatus pictured below functioned to launch a ball off a table and onto a piece of carbon paper which marked the landing point of the ball. The ball lands on flat ground or the first portion of the experiment then on an inclined piece of wood for the second portion marking the carbon paper on both.

To begin the experiment we launched the ball from the top of the v-channel held by the column in order to see where the ball would hit the ground. Once the position was recorded we placed a piece of carbon paper to see where the ball relatively lands. This was done 5 times in order to have an average distance from the table to the landing spot of the ball. The distance from the carbon markings to the edge of the table was measured to be 76 cm in length and the height as 94 cm. These measurements allowed us to find the the ball's launch speed using the kinematic equations

Δy = (1/2)gt^2

Δx = (Vix)t

By substituting in our values for x and y we receive a value for a horizontal velocity

0.94 = (1/2)(9.8)t^2

t = 0.44 s

0.76 = (Vix)(.44)

Vix = 1.73 m/s

The launch speed of the ball is 1.73 m/s

The second experiment in essence is the same but with the difference of adding an inclined wooden board at then edge of the table. We need to derive an expression that allows us to determine where the ball lands relative to the board. Once again using kinematic equations we determine that:

x = d cos(α) = (Vit)t

y = d sin(α) = (1/2)gt^2

[(Vit)(t)] / cos(α) = [(1/2)g(t^2)] / sin(α)

tan(α) = (gt) / (2Vix)

tan(α) = [g(d cos(α)] / [2(Vix^2)]

d = [2(Vix^2)tan(α)] / [g cos(α)]

This is our expression for the distance the ball hits the board. We are able to calculate the value by substituting the values we know and measuring the angle the board makes with the floor which is 48 degrees are result is this.

d = [2(1.73^2)tan(48)] / [9.8 cos(48)]

d = 1.01 meters

After conducting the experiment we find that the average measurement of the end of the table to the carbon markings is 1 meter meaning our expression was in sync with the experimental value only a centimeter in difference.

In conclusion this experiment shows how kinematics help in predicting projectile motion even in unexpected situations. By finding the ball's initial horizontal velocity and measuring the distances it traveled we were able to predict its trajectory on an inclined plane before conducting the experiment.