17 November 2013 AP physics laboratory 1. Title
The investigation on the range, time, initial height, initial velocity, angle of throw, horizontal velocity and vertical velocity of projectile motion 2. Abstract In this laboratory, we measure the range, time, initial height, and initial velocity, angle of throw, horizontal velocity and vertical velocity firstly. After analyzing the measurements and calculations, we find out the conclusions about the relationships between these variables. 3. Interaction Our target is to find out and summarize the relationships between the variables in the projectile motion include range, time, initial height, initial velocity ,angle of throw, horizontal velocity and vertical velocity with the formulas that we have learned from the class. 4. The experiment
Prepare a new tennis ball. Then add some detergent powder to the tennis ball. Thus when the ball falls and hits the floor, it will leave a point that has white mark on the ground. 2. Throw the tennis upward and begin to time. 3. As soon as we hear the voice of the strike, which implies that the tennis falls to ground, stop timing and record the lasting time in the rough data sheet. 4. Use a soft meter ruler to measure the distance between my partner standing positions and where the balls fall into ground and left white mark. 5. Use the ruler to measure the height of my partner; record the value as the Initial Height in the rough data sheet.
6. Adjust our force to throw the tennis again in order to change the range and the lasting time.
7. Repeat procession 1 to 6 until we get enough data.
8. Collect the data and finish the analysis of the data. 5. Experiment conclusion and discussions
Formula used in calculations
Horizontal Velocity: r／t Vertical Velocity: Angle of the Throw: Initial Velocity: Expression of Range Range: R=（2V0²／g) sinθ cosθ R= (V0²／g) sin2θ R=v * t * cosθ Either or can be used since Horizontal Velocity does not change at all. 6. Addendum
The angle that produce greatest range (ignore air resistance) If we combine the function Range= R=v * t * cosθwith t=(2V0／g)sinθ together, we can get R= (V0²／g) sin2θ. Because V is fixed, the value of sin2θ is critical. With a graphing calculator, get the maximum value of,sin2θ,1, with θ equals to 45. Then we can prove that the angle that produces greatest range is 45.
Maximum range achieved in the angle that produce greatest range and the reason why the experimental result does not match it ( according to the first conclusion in the addendum )
If we use the function R= (V0²／g)sin2θ, and sin2θ=1. We suppose that the Velocity is 5m/s, the Range will be s²／9.81, which equals to 2.548m.
7. Data Table
Initial Height: Soft meter ruler
Range: Soft meter ruler
Methods of measurement:
Initial Height-the height of my partner
Range: the distance from the white mark of the impact point to my partner
Time: the whole time interval that the tennis keeps the projectile motion
Methods of calculations: we use EXL to calculate the data automatically)
8. The graph of the horizontal