PhysicsLAB: Video Lab: Two-Dimensional Projectile Motion

Introduction

In this lab you will be examining data taken from the video entitled (Part 1 of 2) An introductory Projectile Motion Problem with an Initial Horizontal Velocity produced by Flipping Physics. The following lab implementation was designed for use in my Honors Physics I and AP Physics 1 classes and only represents one method of analyzing the video. Before taking any measurements, view the video several times to acquaint yourself with its scenario and background information regarding two-dimensional projectile motion.

At this point you should have familiarized yourself with the experiment's scenario. A ball was released from a window of a car moving at a constant velocity of 10 miles/hour across a parking lot. Two cameras recorded the ball's behavior: one was attached to the car's window observing the ball's trajectory relative to the car, and a second camera was stationary recording the ball's trajectory relative to the parking lot. The goal is for the passenger to release the ball at the appropriate moment for the ball to land in a stationary bucket. Our goal during this lab is to understand how the horizontal and vertical motion of a projectile have different properties while occuring simultaneously and independently.

(1) According to the frame of reference of the camera attached to the moving car which statement correctly describes the "path" of the ball as it fell?

it stayed directly under the camera and fall straight down next to the car
it failed to keep up with the car's forward motion and followed a parabolic trajectory landing behind the car
the ball followed a diagonal, linear trajectory and arrived at the bucket simultaneously with the car

Explain your previous choice.

(2) According to the frame of reference of the camera that was stationary in the parking lot, what did the ball's trajectory look like as the it fell?

the ball had a parabolic trajectory and arrived at the bucket after the car has previously passed the bucket's location
the ball had a parabolic trajectory and arrives at the bucket simultaneously with the car
the ball fell straight down and missed the bucket
the ball followed a diagonal, linear trajectory and arrived at the bucket simultaneously with the car

Explain your previous choice.

Refer to the following information for the next three questions.

Shown below is a screen capture from the video (taken at 8:09) that has been marked up by the film maker with the actual measurements for the ball's vertical drop and its range. In this section you will determine the time the ball spent in the air and a scaling factor to convert measurements made in centimeters on the screen capture to the actual distances in meters that were occuring in the actual physical experiment.

Calculate how much time passed as the ball vertically fell the designated 0.7 meters between its point of release from the car's window and the top of the bucket.

Print the screen capture and measure with a centimeter ruler the distance labeled 0.7 meters. Express your answer to the nearest 1/10^th of a centimeter. Remember that larger printouts will yield better measurements!

Based on your previous measurement determine your scaling factor that will convert your measurements from your printout that were in centimeters to meters; that is, 1 cm = ______ meter.

Refer to the following information for the next seven questions.

You are now going to create a grid locating the horizontal and vertical positions of the ball's center of mass as it moves into the bucket. Your final picture will look similar to the diagram shown below. Note that the first "ball" has a vertical and a horizontal position of (0,0).

Using the "0" positions shown on the gridded diagram, measure the ball's cumulative horizontal displacement across the page. Record your results in the data table provided below first in centimeters and then converted into meters.

ball	cm measure	meter conversion
1	0	0

What was the difference (in meters) between your final range and the 1.7 meters shown on the screen capture?

Why was this difference expected?

Hopefully you noticed that the ball's successive horizontal positions were more or less equally spaced. Using that observation calculate a reasonable time interval, ∆t, between each position.

What would a graph of position vs time for the ball's horizontal motion look like?

linear with a negative slopelinear with a slope of zerolinear with a positive slope

Create this graph in EXCEL and reports its slope in m/sec.

Convert the value of your slope in the previous question to miles/hour.

What attribute of the car's motion does your previous answer represent?

Refer to the following information for the next seven questions.

Repeat this process for the vertical measurements of the ball's center of mass. Note that all of your measurements in this section should be negative since the video does all of its analysis with "down" representing a negative direction.

ball	cm measure	meter conversion
1	0	0

What was the difference (in meters) between your final vertical displacement and the 0.7 meters shown on the screen capture?

Why was this difference expected?

What would a graph of the ball's vertical displacement vs time look like?

linear with a negative slope
parabolic opening downward
linear with a slope of 0
parabolic opening upward
linear with a positive slope

Now return to your EXCEL workbook and plot a graph of vertical displacement vs time squared. This graph should be linear. What is this graph's slope in m/sec²?

Based on the equation s_y = v_ot + ½at², the slope of s_y vs time² should equal one-half of the acceleration due to gravity. What is your slope's percent error?

Refer to the following information for the next five questions.

EXTENSION. Using energy methods determine the ball's final resultant velocity as it entered the bucket. Take the zero level for potential energy to be the top of the bucket. Let the mass of the ball be 14.53 grams. In this section, give all of your energy answers in joules (J).

What givens do you need to calculate the ball's initial PE just as it was released?

What givens do your need to calculate the ball's initial kinetic energy just as it was released?

What was the ball's total energy (PE + KE) when it was released?

What type of energy did the ball have just as it entered the bucket?

If air resistance can be considered negligible, what was the ball's actual speed (resultant velocity) as it entered the bucket? If you wish to examine the drag forces on the lacrosse ball you should examine this second video.

Conclusions

The ball's horizontal behavior is classified as

uniformly acceleratedconstant velocity

The ball's vertical behavior is classified as

uniformly acceleratedconstant velocity

Explain how time unites the ball's horizontal and vertical behaviors.

Explain why energy methods allow you to "blend" the ball's horizontal and vertical behaviors.