Lab 4 Trajectories

In this lab, we were going to predict the impact point of a ball on an inclined board with our understanding of projectile motion.So we need to set up a model to make the ball launching in same direction and speed.
As what picture shows:

And then, we need to tape a carbon paper to the floor about where the ball landed. After this, we launched the ball five times from the same high as before and verify that the ball lands in virtually the same place each time.

Now, because we need to calculate the velocity of the ball, when the ball launches, we need to measure the height of the ball falling, the distance of the ball lands from the table's edge.

With hanging a plumb bob, we also get:

the height of the bottom of the ball when it launches: 0.94 m

the distance of where the ball lands from the table's edge: 0.755 m

=>velocity:

we already known the distance, but we did not the time it falling.

Thus,  from

Vo= 0 m/s, g= -9.8 m/s^2 =>

=>

And,we plug the time and distance into equation:

In this lab, our goal is predicting the impact point of ball on an inclined board. And we have known the Vo and angle of the inclined board.

For predicting impact, we had to create two equation to describe the path of falling ball and the inclined board.

Falling ball:

inclined board:

After solving this two function, we can predict the point (x,y) where the ball will impact the board.And we can get the distance

In experiment, we place a board so that it touched the end of table and floor, and attach a piece of carbon paper to where the ball may impact to board. Finally, find the point and measure the distance, and we found the theoretical value for d is bigger than experimental one, but they are almost same.