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Physics: High School18 chapters | 212 lessons

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Lesson Transcript

Instructor:
*David Wood*

David has taught Honors Physics, AP Physics, IB Physics and general science courses. He has a Masters in Education, and a Bachelors in Physics.

After watching this video, you will be able to define projectile motion and use the equations of projectile motion to make predictions about motion in a real-life scenario. A short quiz will follow.

**Projectile motion** is motion in two or more dimensions where the only force is gravity. A classic example would be a cannon being fired at an angle. Such a cannonball has a velocity both up and sideways. And the cannonball is, in this case, the projectile.

In other lessons, we introduced the equations that govern 2D projectile motion. Here they are again.

Equations in the Y-Direction:

vf = vi + a * t

*y* = vi * t + ½ a * t^2

*y* = vf * t + ½ a * t^2

vf^2 = vi^2 + 2a * *y*

*y* = (vf + vi) t / 2

Equations in the X-Direction:

v*x* = *x* / t

In the *y*-direction, we have an acceleration, so we can use the kinematics equations of constant acceleration. This acceleration is caused by gravity, so *a* will be equal to -9.8 m/s/s on Earth. And in the *x*-direction, once the object is launched, there are no forces, so the cannonball (or whatever it is) continues at a constant velocity. For this reason, we only have this one equation in the *x*-direction. But now it's time to use these equations in a real-life scenario. It's time to investigate projectile motion!

For this physics lab, you will need:

- A marble
- A smooth table
- Materials to create a sturdy ramp (for example, a plank of wood and some books)
- A target printed from the Internet, with several rings
- A stopwatch
- A tape-measure or ruler

Once you have your materials, set up a sturdy ramp on top of the table. Leave at least 30 centimeters (ideally longer) between the end of the ramp and the edge of the table. The more smooth the transition from ramp to table, the easier the lab will be.

Place your printed target on the floor, and observe your magnificent set up. Your goal is to calculate where on the floor to position your target, so that your marble will roll down the ramp, across the table and hit the bulls-eye on the floor. But you are not allowed to do test runs. The marble cannot leave the table until you've done all your calculations and are ready to go. If you let it do so, you lose the game. You are allowed to take whatever data you want on the tabletop. You can roll the marble down the ramp and across the table, so long as it never leaves the table. You can also take measurements with the ruler and stopwatch.

Using the equations for projectile motion and whatever data you are able to take, calculate where to place the target on the floor. The center of the target represents an A grade for the lab, the next ring is a B and so on. Can you get an A the first time?

If you fail, you must change the height of the table by putting a book underneath each table leg, and start again. If you fail again, you must change the slope of your ramp. If you fail a third time, it's game over.

So now, it's time to pause the video and get started. Good luck!

If you're listening to this part of the video, you've already tried the lab yourself. If not, go back and try it. There's no fun in cheating. But if you need a hint, I'll give you one: The first step is to figure out how fast the marble is going as it moves across the table. That will give you a velocity in the x-direction.

Okay, so if you've already figured that out and successfully completed the lab, here's the solution.

**Step 1:** Measure the speed of the marble moving across the horizontal part of the table. Measure the distance using a ruler or tape measure, and measure the time using the stopwatch, average your numbers, and then divide the distance by time to get the speed. So, here you're figuring out how fast it's moving across the table. In the equations, that number is your V*x*, your velocity in the *x*-direction.

**Step 2:** Measure the height of the table surface above the floor. That's your *y*-variable.

**Step 3:** Realize that a, the acceleration, is -9.8 because the marble is falling under gravity, and note that down. Also realize that when the marble leaves the table, the velocity in the *y*-direction is zero, because it starts out moving directly horizontally. So vi equals zero.

**Step 4:** Calculate the time of flight from the edge of the table to the floor using:

*y* = Vit + 1/2at-squared

- Vi equals zero
*y*equals the height of your table- a equals -9.8

And, you can solve for t.

**Step 5:** Plug in your time of flight, t, and your velocity as the marble leave the table, v*x*, into the *x*-direction equation, and solve for *x*, the displacement in the *x*-direction (v*x* - *x* /t or v*x* * t = *x*).

**Step 6:** Measure your *x* distance away from the very edge of the table, across the floor (you will need to line this up really carefully). Then position your target at that spot, being careful to also get the sideways position right and stay in-line with the ramp.

**Step 7:** Let go of your marble and enjoy your sweet victory.

If you did the above, and it still didn't quite work, there are a couple of likely issues. The first is that your time measurements weren't accurate enough. The stopwatch is the biggest source of error in this experiment by far. Another possibility is that the marble is drifting sideways. . . try to build your ramp in ways that reduce the chance this will happen. The faster the marble goes, the less it will drift, but also the harder it is to measure the time. Last of all, be sure to check your math super carefully.

**Projectile Motion** is motion in two or more dimensions. A classic example would be a cannon being fired at an angle. Such a cannonball has a velocity both up and sideways. Here are the equations that can be used to describe projectile motion.

Equations in the Y-Direction:

vf = vi + a * t

*y* = vi * t + ½ a * t^2

*y* = vf * t + ½ a * t^2

vf^2 = vi^2 + 2a * *y*

*y* = (vf + vi) t / 2

Equations in the X-Direction:

v*x* = *x* / t

In the *y*-direction, we have an acceleration (of -9.8 down) and so we can use the acceleration equations. In the *x*-direction, we have a constant velocity and so just we just have that one constant velocity equation.

In today's lab, we applied these equations to a real-life scenario by rolling marbles off a table and using equations to predict where they will land on the floor. With so little friction on a marble rolling across a smooth table, the calculations should work out if you take your measurements carefully. While physics experiments do have a tendency to go wrong, this one proves pretty well that physics. . . just works!

Study gravity and projectile motion via this lesson, then find out how well you can:

- State the definition of projectile motion and cite an example
- Write the equations that describe projectile motion
- Complete an experiment using marbles in order to prove these equations

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Physics: High School18 chapters | 212 lessons

- Forces Imposed on Objects: Physics Lab 3:16
- Newton's First Law: Physics Lab 4:56
- Measuring the Speed of an Object: Physics Lab 3:53
- Graphing the Motion of Objects: Physics Lab 3:17
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- Gravity & Projectile Motion: Physics Lab 6:03
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