Kinematics Activity
Target Practice

Purpose:

To predict the landing spot of a horizontally-projected projectile.

Discussion:

If you know the height of a table, you can calculate the time required for a ball to fall from the table to the floor. If you know the velocity of the ball as it leaves the table, you can calculate the distance from the table at which the ball will hit the floor. You can find the velocity of the ball if you know the time it takes to roll a measured distance on the table.

In this lab, you will place a tin-can target at the predicted landing spot of the ball. If the ball lands in the can the first time, you get credit for the lab.

Notes:

•  Accurate measurement and precise calculation are very important in hitting the target. Be sure to use 9.80 m/s² (= 980 cm/s²) for "g".
  
  
• Credit is given in this lab for hitting the target the first time the ball hits the floor. Be sure that you catch the ball before it leaves the table. If the ball hits the floor at any time before your "official launch", you must change your launcher to produce a significantly-different velocity for the ball, and start over.
  
  
• If the ball misses the target to the right or left, it will still count as a hit.

Equipment:

small sphere	meter stick	stop watch	string
tin can	tape	small weight	plastic ruler or book
calculator	worksheet (ClarisWorks)

A calculation worksheet (ClarisWorks) is available to help you organize your calculations.

Procedure:

1. Devise a "launcher" for the ball from a ruler or book - anything with a smooth groove in it that the ball can roll down. Find a starting point on the launcher that gives the ball a reasonable velocity.
   
   
2. Place 2 pieces of tape 30-50 cm apart on the lab table in the path of the ball. This is distance "d" in the diagram above. Record this distance. The distance that you use needs to be a compromise:
   
   
   • If the distance is too short, you will not be able to get an accurate time for the ball to cover the distance, and your velocity will not be accurate.
     
     
   • If the distance is too long, friction will slow the ball appreciably by the time it reaches the edge of the table, and your calculated speed will not be the actual speed that the ball has when it leaves the table.
     
     
3. Measure the time (t_roll) it takes the ball to cover this distance. It would be a good idea to time several trials and calculate the average time. Record your data in a data table.
   
   
4. Calculate the speed, v_x, of the ball as it rolls across the table. Show your calculation.
   
   
5. Carefully measure the vertical distance from the top of the lab table to the top of your target. This is "h" in the diagram above. Record this distance.
   
   
6. Calculate the time (the falling time, t_fall) it will take the ball to fall from the table top to the target. Show your calculation.
   
   
7. Calculate the horizontal distance that the ball will go during the time it takes to fall to the target. Show your calculation.
   
   
8. Locate the point on the floor directly below the edge of the table top where the ball leaves the table. You can do this accurately by making a "plumb line" from a small weight and a string.
   
   
9. Measure the horizontal distance that the ball will go on the floor, and place the target at that point.
   
   
10. Call your instructor. While you wait:
    
    • Are your measurements consistent and reasonable?
    • Did you check your calculations?
    • Is the target distance reasonable?