Baseball (Catherine Nicholas)

Title: How Far Can I Throw a Baseball?

Principle(s) Investigated: projectile motion, kinematicts (in two dimensions), vectors

Standards :

Physics 

Motion and Forces 

1. Newton’s laws predict the motion of most objects. As a basis for understanding this concept: 

a. Students know how to solve problems that involve constant speed and average speed. 

e. Students know the relationship between the universal law of gravitation and the effect of gravity on an object at the surface of Earth. 

i.* Students know how to solve two-dimensional trajectory problems.

j.* Students know how to resolve two-dimensional vectors into their components and calculate the magnitude and direction of a vector from its components. 


Materials: Stopwatches, baseballs, meter sticks, field (preferably a football field with lines every 10 yards).

Procedure:
  • Students must start by measuring the distance from the ground to the height where they will naturally release a ball.
  • Students then take turns being the thrower, timer, and measurer.  Students will use the data from when they are the thrower, as they are trying to figure out how fast they can throw a baseball.
  • The thrower is going to stand on one of the lines on a football field and throw a baseball.
  • The timer must start the stopwatch as soon as the baseball leaves the thrower's hand and must stop the stopwatch as soon as the ball hits the ground.  This time is recorded on the thrower's paper.
  • The measurer must place the ball exactly where it had first hit the ground and measure the distance it landed from the thrower.  The lines on the field help, because the measurer can just measure from the closest line and know how many yards are between the thrower and the closest line. (For example, if the thrower is on the 10 yard line, and the ball lands just past the 30 yard line, then the measurer already knows that the ball went 20 yards plus a little bit and just has to figure out how long that little bit is and add it to 20 yards.)  The distance is recorded and distance are changed into meters.
  • This process is repeated until everyone has had a chance to throw the ball.
  • With their data, students solve for the initial velocity in both directions, then solve for the magnitude and direction of the initial velocity.  Students then solve for the maximum height that their ball went.

Student prior knowledge: Students must understand how to solve one dimensional kinematics problems, students must also understand how to use vectors to find magnitude and direction.

Explanation: Students will be able to solve for their initial velocity using the three kinematic equations: 
x=vit+(1/2)at2 
vf=vi+at 
vf2=vi2+2ax

Questions & Answers:
If you want to throw the ball as far as you can, at which angle should you release the ball?  The ball should be released at about a 45 degree angle, then the ball will go up enough to stay in the air as long a possible, before gravity brings it to the ground, and it will have enough horizontal velocity to travel far in the amount of time that it is in the air.
What are some factors that cause the calculated initial velocity to be different from the actual initial velocity? The calculated numbers are likely different from the actual values because there is air resistance, which our equations do not take into account.  There is also human error in the flight time, as a person will not get the exact moment that the ball leaves the person's hands and the moment it hits the ground.  It may also be difficult to get an exact distance, as the ball will likely bounce and roll as it hits the ground and it is up to the measurer to figure out exactly where it landed.  
Explain how you knew that you could solve for all of the missing values.  In both the horizontal and vertical directions, we had three out of the five variables known from our measurements, as we know from kinematics, if we have any three values, we can always solve for the other two.  After solving for the missing values, our knowledge of vectors allows us to find the magnitude and direction of the initial velocity.

Applications to Everyday Life: Knowing theses principles can be applied to many sports, anything where a ball is going through the air (soccer, football, baseball, basketball, volleyball, tennis, golf...), it can help students to understand the principles at work for getting the ball from one place to another.  These concepts can also be applied to hitting a target (you must aim slightly above your target, because gravity will pull the item down).  

Photographs: Include a photograph of you or students performing the experiment/demonstration, and a close-up, easy to interpret photograph of the activity --these can be included later.

Videos: Include links to videos posted on the web that relate to your activity. These can be videos you have made or ones others have made.

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Norman Herr,
Sep 12, 2011, 8:16 AM
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