Activity: Trajectories

Activity: Trajectories
Purpose: Using the understanding of projectile motion to predict the impact point of the ball on an inclined board.
Materials: We need aluminum "v-channel", steel ball, board, ring stand, and camp to set up the following apparatus.

 We also need paper and carbon paper so we can clearly record the collision point of the steel ball.

Procedure:
To make sure the angle of the apparatus doesn't change, and to make sure our ball has exact the same horizontal initial velocity when it take off from the table, we have to carefully tape every joint of the apparatus, and make sure we launch the steel ball at the exact same point on the track.

First of all, we need to remove the inclined board and let the ball hit the ground, so we can find out the initial horizontal velocity of the ball when it take off from the table.

Then, we will set up the inclined board with a certain angle, and use the initial horizontal velocity we found and the inclined angle of the board to predict the point the ball collide with the inclined board.

Finally, we will let the ball go with the inclined board installed on the apparatus, and compare the experimental distance it travel along the board to the one we predicted.

Measure and Prediction:
We first put the carbon paper on a sheet of paper at the point the ball will most likely hit. We launched the steel ball at the exact same point on the track, and measured and record the horizontal distance it traveled from the table in 5 trials. We took the average of the 5 trials and we got that the horizontal distance it traveled after taking off from table is 66.9cm, and we also measured the height of the table and found it was 96.5cm.

We then did the following calculation to get the initial horizontal velocity when the ball take off from the table:

The initial horizontal velocity v0 = 1.51 m/s
The angle of between the inclined board we set up and the floor is 51.6 degree.
With these two information we did the following prediction:

Our theoretical distance the ball traveled along the inclined board d = 0.95 m

Finally, we tape the carbon paper on a sheet of paper and put them on the board where the ball would most likely hit, and we again launched the ball at the exact same point on the track as we earlier did, and record and take the average of the  distance the ball traveled along the board in 5 trials. The experimental distance the ball traveled along the inclined board d = 0.91 m ± 0.1 m.
%error= (0.91-0.95)/0.95*100% = -4.2%
Conclusion:
In this activity, the final lab result has a -4.2% error compare to the theoretical prediction we made. The difference might be caused by the imprecision measurement of the height of the table and the distance the ball traveled. We also found that our table was a little inclined, which would cause the initial took off horizontal velocity to be a little faster. Finally, in the prediction we made, we didn't take air resistance into account.