Trajectory Lab

Trajectory Lab

Tyler Moore

Ryan Gibbel, Dean Defuria

Physics, Block 2

Mr. Elwer

Trajectory Lab

Background:  

In performing this lab we will calculate the speed at which a ball is thrown using an "angle measuring gun" tool to measure angles and a tape measure to measure the ball's displacement. The ball is thrown from about 2 meters above ground level and hence the fact that gravity will cause it to fall the ground.  We will use the following: trigonometry, projectile motion, time of flight and free fall acceleration to determine the the angles and displacements in order to find the velocities and overall speed at which the ball was thrown.

Materials:

2 Angle Measuring Guns (and people to use them)

3 Cones Tennis ball (1 person to place them)

2 Tennis Balls (1 person to accurately throw it twice)

1 Tape measure

Experiment and Design:

The experiment was setup on the rubber run-way of the Track Jumping pit.  Placing the thrower at one end and then at an accurate distance away the recorder. The other 2 group members, stand a certain distance away from the middle of the throwing lane to calculate the angle at the projectile's highest point or peak. The thrower will throw the tennis ball, with some sort of arc and accuracy multiple times. The recorder will place a cone at the exact place the ball lands and record that displacement.

Procedure:

1. Thrower stand at one end of the jumping run-way with tennis balls.  Recorder at other end with 2 cones.  Place the 2 angle measuers, with Angle Measuring Guns, approxiamtely 10 meters away, from midpoint of the trajectory.
2. Thrower throws the ball with arc and accuracy.
3. The recorder marks its exact landing spot and calculates the displacement.  At the same time that the ball is in motion the angle measaurers will be measure the angle when the ball is at its highest point. 
4. Repeat this procedure so that it will be done 2 times to get an average in all categories.

Data Table: Trials 1 2 Distance 23m 23.4m Angle 33.0 degrees 33.0 degrees To find height from ground: since the angle is the same both times, we know the average angle is 33.0 degrees. 2.00m+10.0mtan33.0deg=8.50m, but DeltaY is negative, so DeltaY=-8.50m Now height is known, time can be solved for. This is key because time is what links horizontal and vertical motion together.  DeltaY=Viy+(aDeltat)/2 -8.50=DeltaY, so -8.50m=0+((-9.81m)t2)/2,   -17.0m/-9.81m=t2   t=1.32s Solve for VelocityY, Vy=Vit + at = 0 + (-9.81)(1.32) = -13.0m/s Velocity is Displacement over time, so Vy=DeltaY/t,  Vy= -8.50/1.32=-6.44m/s Now there are both components of Initial Velocity, so the Pythagorean formula can be used. Vi=Sqroot(6.442+13.02)=14.5m/s *note* after this is square rooted, it is plus or minus. But the ball was thrown in a forward motion and because of this and other information, we know it is positive initial velocity. Now all that is left to be solved is the angle of the throw. Angle=tan-1(8.5-2)/11.6=29.3degrees Conclusion: A key factor in this lab is that the ball was not thrown from ground level, but rather at 2 meters above the ground.  Therefore, it was neccessary that the angle measurements be taken from 2 meters above the ground in order to make it more accurate.  Previous to this lab, we only knew how far the ball traveled and the angle of its trajectory.  However, we we calculated the hieght of the ball at its peak, the amount of time the ball was in the air, the velocity in bot the Y and X directions, initial velocity, and the angle in which the thrower threw the ball.  Another finding this lab provided was the distinction between the physical world and the real world and although certain things aren't factored into the physical world when compared to the real world they are still very accurate.  For example, wind resistance was not factored into our experiement and yet, our results were close to those if the experiment has been done in the real world.