# Projectile Motion

You have probably watched a skater jump a set of steps. Like all objects under this influence of gravity the skater follows a projectile motion path as he falls through the air. In this lab, you will be rolling a ball horizontally off the edge of a table. Like the skater, the ball will follow a projectile motion path.

### Preliminary Questions

As with all problems, we want to think about what may happen before we devise an experiment. You can think about things in a scientific manner. These are commonly called 'Thought Experiments'.

We want to simplify things first. Instead of the more complicated problem of a skater rolling off a flight of steps, lets first think about a skater stepping off a tall platform and falling straight down. You can ignore air resistance for now.

- What information do you need in order to predict how much time it would take for the skater to hit the ground?
- If you traveled to another planet where the gravitational acceleration was larger, would that make a difference in the time it takes the skater to fall from the same height? Explain.
- If the skater stood on a taller platform and stepped off as before, would the time to hit the ground change? If so, how?
- What if, instead of stepping off the platform, the skater jumped up first, how would this change his time in the air?
- What if, instead of stepping off the platform, the skater jumped down, how would this change his time in the air?
- What equation did you learn in class for relating the vertical fallen distance to time, acceleration, and initial velocity for a falling object? Use t for time, a for acceleration, v0 for initial velocity, and d for vertical distance.
- Rewrite the equation for the special case of an object dropping from rest.
- Since distance is related to the square of time, how does the distance traveled per second change each second? Hint: Think about whether the distance the skater falls at the beginning of the motion is the same, greater than, or less than the distance he falls at the end of the motion.
Now think about the more complicated problem of the skater jumping a flight of stairs instead of simply stepping off a platform. Now the skater is moving forward when he starts to fall. (You should still ignore air resistance.)

- Does this initial horizontal motion change the amount of time it takes the skater to land on the sidewalk? Explain. Hint: Remember what your book discussed about the similarities between dropping a bullet vs. firing a bullet horizontally out of a gun.
- What would you need to measure in order to predict how far from the top of the steps (horizontally) the skater will land?
Now let's forget about the skater and concentrate on today's lab. Today you will design and test an experiment in which you roll a ball off the edge of a table and predict where is will land on the ground. The first order of business is to figure out how to determine the velocity of the ball the instant before it rolls off the table. As with the skater, you could measure the velocity with a motion detector, but it turns out this is actually kind of difficult to do.

- Can you tell me why a motion detector is perfect for the last lab we did, but would cause problems here? There are several reasons.
Since using a motion detector is a bit of a hassle, we will instead use something called a photogate. The photogate acts like a high-tech laser security system which triggers when the ball interrupts the path of the laser beam. When an object passes between the arms of the photogate, a signal is sent to the computer. If an object passes through two photogates, then the microcontroller will receive two signals, one after the other, and can then calculate the amount of time that has elapsed between the first signal and the second signal.

- For this particular experiment, why is this method of timing better than using a hand-held stopwatch?
- Examine your BeeSpi photogates. Can you see the two sets of photodiodes? The photogates will display the velocity of the rolling ball.
- Design an experiment that allows you to predict how far a ball will travel horizontally when rolled off a table. Be sure to tell me all the things you need to measure and all the things you need to calculate. You should be able to think back to all the questions you answered about the skater and relate it to the ball, you have already determined most of this stuff and you should just be applying it to a new situation.
- In the above thought experiment, what two equations will you need to use? List what quantities you need to measure in order to make your prediction.
- Since your experiment should be repeatable, how will you ensure that the ball is traveling at the same speed each time you perform the experiment?
NECESSARY EQUIPMENT

- two photogates
- two meter sticks
- ramp
- plastic cup
- steel bearing

### I. Finding The initial Horizontal Velocity

Setting up the photogates: You will roll the ball bearing down the track and through the photogates. Place the photogates at the very end of the track, so that the velocity you calculate most accurately represents the speed of the ball as it exits the track. Do not let the ball hit the floor! Catch it as it is coming through the photogates.

Click the "Start" button to turn the timer on. If the units do not default to m/s, press and hold the "start" button. Use this timer to directly determine the velocity of your ball bearing. Press "Start" again when you are ready to collect data. To test, pass your finger through the photogates.

- How does the BeeSpi timer calculate velocity? Think about what the timer is directly measuring.
- Please do this at least 10 times. Release the bearing from the same point each time. Be sure to write down all 10 values, including units. Calculate an average horizontal velocity. Show all your work!

### II. Calculating the Horizontal distance

- Knowing the average horizontal velocity of the ball bearing, calculate how far from the table the ball will land on the floor. Use the method you described above to mathematically determine where the ball will hit. Show me all your work, and define each parameter!
- After you predict where the ball will land, set a cup there. Now perform the experiment again to see if you hit the cup! Were you successful! If not, figure out why and try again!!!!
- Should you expect any numerical prediction based on experimental measurements to be exact?
- Would a range for the prediction have been more appropriate? Explain.
- You accounted for variations in the velocity measurement in your distance prediction by taking an average time. Are there other measurements you used which affect the distance prediction? What are they?
- If air resistance was significant, how would this change your predictions?
- Combine what you have learned to derive one single equation, without the time parameter in it, for determining where the ball will land.
- Would your results be any different if you repeated this experiment on the moon? Why?

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