C-1Projectile Motion and the Range Equation

1Analyzing the motion of the marble in two dimensions

a. Use the diagram to explain why projectiles travel in a curved path called a trajectory.

b. How does the marble’s velocity in the x change over the time of the flight?

c. How does its velocity in the y change over the time of the flight?

2Understanding the velocity equations

a. Write the equations for the x and y component of the velocity.

b. Rewrite the Equations 1a-2b leaving out any terms that are zero, substituting the equations from (a) above, and using –g for the acceleration in the y axis. Be sure to write all four equations.

c. Solve for the time it takes the marble to reach 0 displacement in the y (the ball has gone up, and come back to the ground). Write out this equation.

d. Substitute this into the equation for displacement in the x, and write this equation.

3Setting up the marble launcher

4Doing the experiment

Spring Setting 1
Launch Angle
(degrees) / Range
(m) / Ball Diameter
(m) / Time from A
(sec) / Initial Velocity
(m/s)
0.019
0.019
0.019
0.019
0.019
Spring Setting 2
Launch Angle
(degrees) / Range
(m) / Ball Diameter
(m) / Time from A
(sec) / Initial Velocity
(m/s)
0.019
0.019
0.019
0.019
0.019
Spring Setting 3
Launch Angle
(degrees) / Range
(m) / Ball Diameter
(m) / Time from A
(sec) / Initial Velocity
(m/s)
0.019
0.019
0.019
0.019
0.019
Spring Setting 4
Launch Angle
(degrees) / Range
(m) / Ball Diameter
(m) / Time from A
(sec) / Initial Velocity
(m/s)
0.019
0.019
0.019
0.019
0.019

5Comparing theory predictions to measured data

Initial Velocity
(m/s) / Launch Angle (degrees)
x(predicted)
x(measured)
x(predicted)
x(measured)
x(predicted)
x(measured)
x(predicted)
x(measured)

a. Make a graph showing the range vs. launch angle for several different initial velocities. Use four different colors for the four different launch velocities. Place circles around the points that are actual measured values, and squares around the points that are the theoretical values. Draw curves or straight lines (whichever is appropriate) only for the theoretical points. Use the graph paper provided.

b. How does your theory compare with your measurements?

c. Is there a consistent deviation between theory and experiment? That is, does the difference between the theoretical and the experimental data seem to depend on something in the experiment and not just random.

d. Consistent deviations indicate that something is missing from the theory. What is missing, and why does it have the observed effect on your results?

Questions

1A marble launcher is set up on the floor using notch 3 and an angle of 45o. The marble launcher is launched and the range is measured. The launcher is then taken off the floor and put on a nearby table. It is again set for notch 3 and 45o. Will the two flights be the same or different? Explain.

2Where along the trajectory is the vertical component of the velocity of the marble zero?