Bull's Eye Predicting a Trajectory

Predicting a Trajectory

Problem:

How can you predict the landing position of a projectile launched horizontally at any speed?

Materials:

Stopwatch, meter stick, ramp, steel ball (or marble), catch cup, washer (or plumb bob) and thread.

Note: Student must catch the ball while it is in the air during the trials to determine the horizontal velocity of the ball. The ball may not be allowed to hit the floor until the official “shot for the grade”.

Procedure:

Start the ball at exactly the same spot each time to make sure that the horizontal velocity with which the ball leaves the table is the same each time. Determine the horizontal velocity by measuring the time it takes for the ball to roll horizontally along the table and the horizontal distance through which it moves. Make the measurement of time several times. Use the formula dx = vxt to calculate the horizontal velocity. Use the vertical distance, dy, to calculate the time of flight using the motion formula dy = ½ at2. (The initial velocity in the vertical direction is zero). Use this information to calculate the landing position of the ball. Set up equipment as pictured above. All work must be shown on this paper. Instructor must see the calculations and witness the "shot for the grade". The lab grade is based on calculations and accuracy.

Construct a data table that contains the following:

1. Information needed to calculate the ball’s horizontal velocity

2. Information needed to calculate the time of free fall for the ball.

3. Information needed to calculate the distance from the edge of the table for the marble to hit.

4. Calculate a prediction for the ball’s range. Record the experimental value.

5. Instructor should place a cup or small ring (about 8 to 10 cm) on the floor. The students then release the ball from the same place and see if the ball lands inside the ring.

6. If the ball misses the ring by a very small amount, move the ring and try again. If the ball misses the ring by a large amount, recheck the calculations.

Predicting a Trajectory

Teacher’s Notes

Procedure :

The best thing about this lab is that it works! If you have reasonably good tracks, almost all of the students will get the ball in the ring the first time. Hardware stores carry several types of materials used to protect corners of wall board that can be used effectively as tracks. Steel balls can be bought from scientific companies or steel ball bearings can sometimes be found free from a place that repairs big trucks.

The grade should depend upon how close they come to the cup (i.e. first time or not) plus carefully shown calculations.

A track can be constructed using a piece of corner molding, hot wheels track or lawn edging taped to a meter stick, two meter sticks placed side by side , or a ruler with a groove in the center. For the distance “d” on the table it is also advisable to have a track to keep the marble rolling straight. The most important thing about the track is not to have it too steep. If the ramp is too steep and the horizontal velocity quite fast, errors in timing are more likely to occur.

An empty tuna fish can makes a perfect “target” for the ball. The “target” should not be given to the students until they are ready for the “shot for the grade”.

The time interval is difficult for students to measure. If photogates are available the accuracy is improved. Students can use a stopwatch to measure the time the marble rolls along the table. A meter distance works well. Remind the students to catch the marble as it leaves the end of the table. The measurement should be repeated several times, always releasing the marble from the same point on the ramp. Using this data the students can calculate the average value for the horizontal speed as the ball rolls along the table – this is more accurate than any single measurement.

Students use the vertical distance dv to calculate the time of free fall. Using the calculated free fall time and the equation for predicting the range of a projectile (dh = vht) students predict the location of the catch cup for a bull’s eye.

Fairly detailed directions have been given in the lab write-up, but they are not necessary. If a sample set-up is shown, most students can do the lab with brief verbal instructions. The grade can then be based on how close the ball came to the cup. The calculations must be correct if the ball goes into the cup.