15-Mar-2017: Trajectories

Since we have already learned how a free fall object moves, we can draw the trajectory of the object. However, in our reality, the object does not always land in the flat; sometimes, it will land on the incline. Therefore, in today's lab, we did some experiences on a free fall ball with horizontal velocity to see how the trajectories work when landing in an incline.

Purpose:
To use your understanding of projectile motion to predict the impact point of a ball on an inclined board.

Set up:
1. We set the apparatus as following.

2. Then, we put the ball at the top of track, then release it, and collected the data when hit the ground. (Repeat it to make sure at the same point). 

3. Next, we set up an incline to begin our experience. (The slope is 49º ± 1º)

4. Repeat step 2 to make sure to get a similar point. 

Analyze:

In the first part we get the X = 75.5 ± 0.1 cm, H = 96.3 ± 0.1 cm. 

By functions

We can get

then, we get v ≈ 1.703 m/s.

In the incline, we got the functions

Then, we got 

D ≈ 1.038 m , and the real D = 1.055 m 

Propagated uncertainty:

Part 1:

dv ≈ ±0.00331m/s

Part 2: 

dD ≈ ±2.096 m

since the uncertainty for angle is too large, the propagated uncertainty does not really work. 

Conclusion:

Since we have trajectories of free fall objects, we can always predict where will the objects land in any situation, and in a slope and horizontal velocity is known system, we can use the function

to find out the land point. In the meanwhile, if we know the distance and the angle of slope, we can the the initial velocity; if we know the distance and the initial velocity, we can calculate the angle of slope. 

(And the propagated uncertainty does not really work when one the uncertainty is large.)