Lab 2: Investigating Projectile Motion

Lab 2. Investigating Projectile Motion Physics 152 

Prof: Professor van der Veen 

Lab Instructors: Ms. Walker, Mr. Stankovich 

Lab 2: Investigating Projectile Motion 

In this lab, you will do the first part (graphing with Excel) with one partner. For the 

shooting activity, due to lack of space as well as lack of equipment, you will work in a 

group of 4 people with your entire lab table row (two groups of 2 people/group). 

However, you must each turn in your own paper, albeit with the same data. 

Equipment: Make sure you have the following equipment in working order : 

1. Laptop computer 

2. Shooter, ball, and plunger: ALWAYS USE THE "SHORT" SETTING FOR 

SHOOTING IN THIS LAB! 

3. Meter stick 

4. Plain white paper, carbon paper, and masking tape 

Please do not write directly on this set of instructions, but write your 

answers on your own paper. Please RETURN this set of instructions to 

your instructor before you leave. Please DO NOT walk out the door with 

this paper in your hand, but leave it for the next section. 

Part 1. Graphing simulated data of projectile motion, and extracting information 

from the graphs. 

Here are some simulated data for a projectile launched from a height of 2.0 

meters, in the horizontal direction, with some velocity v x . Time is given in seconds, and 

horizontal displacement (x) and vertical displacement (y) in meters. Type these data into 

Excel and graph x(t) and y(t), and then y(t 2 ) and answer some questions. 

time (seconds) x-position y-position 

0 0 2.000 

0.05 0.5 1.988 

0.1 1 1.951 

0.15 1.5 1.890 

0.2 2 1.804 

0.25 2.5 1.694 

0.3 3 1.559 

0.35 3.5 1.400 

0.4 4 1.216 

0.45 4.5 1.008 

0.5 5 0.775 

0.55 5.5 0.518 

0.6 6 0.236 

Jatila van der Veen Page 1 6/16/2009




a) Graph time on the horizontal axis, and graph both x and y as series 1 and series 2. Use 

the scatter plot option. 

b) Describe each graph (straight line, parabola, or what…). 

c) For the graph of x-position, use the Trend Line option. Turn on the feature to display 

the equation. Use the linear function to graph this function and find the slope of the line. 

i. What is the equation that describes this line? (Excel will use "x" but you use 

"t" for time.) 

ii. What is the slope of this line? 

iii. What does this slope represent? 

See simulated data. Vx = 10m/sec = slope of x-motion. Slope represents horizontal 

velocity. 

d) Now copy all the times into another column, say column E, from E2 to E15. In the 

column next to this new column, calculate the squared times in the F column from F2 

through F15. Label this column "t-squared." 

Make a separate graph of the y-values as function of the new variable t 2 . Again, 

use the scatter plot option, and then add a trend line, and turn on the option to print the 

equation on the graph. Use the linear option. 

i. What is the equation of this line of y(t 2 )? Vy = -4.9t 2 

ii. What is the slope of this line, and what does it represent? Slope is ½ the 

acceleration. 

Print out all the graphs on one paper and staple it to your paper of answers. 

Part 2. Shooting, measuring, and predicting 

1. Set the shooter in the horizontal position. Use the attached protractor to be sure that it 

is level. Push the ball into the shooter in the SHORTEST range position (first notch). 

(See Figure 1.) 

Measure the height of the center of mass of the ball in this position to the ground 

and write it down in your lab notebook. 

y total = 





Figure 1. Horizontal shooting arrangement. 

This is the total height through which the ball drops. Last week you timed a ball falling in 

free fall from a height of 2 meters. Use this new height to predict the time it will take 

this ball to fall hit the ground from this height. Write your calculations and answer 

in your lab notebook. 

1 y = gt 

2 

2 

t = 

Put a piece of masking tape on the floor directly beneath the initial position of the ball in 

the shooter, and mark this as x 0 – the initial x position of the ball. 

2. Set up to measure the range: Shoot the ball once or twice and estimate where it lands 

on the ground. Tape some paper to the floor covering this spot, and over the paper, tape a 

piece of carbon paper, face down, so that when the ball hits the carbon paper it will make 

marks on the paper. 

3. Now shoot the ball 20 times (at least). Be sure to 

use the SHORTEST range position of the shooter 

each time. Carefully remove the carbon paper, and 

you should see a nice cluster of dots on the paper. 

With the paper still taped to the floor: 

i. Find the center of the cluster – presumably, this 

will be the darkest spot! 

Figure 2. Circle of dots. 





ii. Draw a circle around the center, encompassing the majority of the dots, and a second 

circle, concentric to the first, encompassing what looks like 95% of the dots, as 

approximated in Figure 2. 

iii. Measure x f as shown on the diagram, from the tape which you placed on the floor 

DIRECTLY beneath the initial position of the ball, to the center of the cluster of dots. 

Write this down in your lab notebook as x final . 

4. Now remove the paper from the floor. Measure the radius of each circle. The radius of 

the inner circle let's say is our "eyeball σ" and the outer radius we'll say is your 95% 

confidence limit. Report your x final as a distance in meters, +/- one "eyeball σ" in cm 

in your lab notebook. 

5. Now, because the time to hit the floor in freefall is the same as the time to travel this 

distance x f you can use your calculated time to fall through y total and your measured x final 

to calculate the initial velocity of the ball after it leaves the launcher. 

⎡ 2y 

⎤ 

x = vxt 

= vx 

⎢ ⎥ 

⎣ g ⎦ 

x x 

vx 

= = 

t 2y 

g 

= Show your calculations and 

answer in your lab notebook. 

This is the total initial velocity, v 0 that we will use in the next section, when we shoot 

at an angle. 

6. Errors: You have found the approximate error in x as +/- "eyeball σ." Now estimate the 

error in your vertical measurement (is it +/- 1 mm = .01 cm? Or what?) which gives you 

your approximate error in t…and estimate your total error in v x . What other 

approximation have we made? 

7. Finally, write all your calculations in a data table, showing measurements and 

calculations: Measurements: y, x final Calculations: t, v x 

I'm looking for them to write out all the calculations, and put the results in a data table. 





Part 3. Shooting at an angle and predicting the range. 

Figure 3. Shooting at an angle above horizontal. 

1. Tilt your shooter at 30 0 . Use the attached protractor to measure this angle. Push the 

ball into the barrel at the SHORTEST position, and measure the new y position. (It 

should be somewhat higher than before.) Again, put a piece of masking tape on the floor 

directly beneath this new initial position, to mark the initial x-position. Record these 

measurements in your lab notebook. 

2. Calculate the horizontal and vertical components of the initial velocity, v x and v y,0: 

v 

v 

x 

y,0 

= v 

0 

= v 

cosθ 

0 

sinθ 

and record these in your lab notebook 

3. Calculations and predictions: 

a. Now the ball will have a parabolic path. We know that the horizontal velocity will be 

constant across the entire path, until the ball collides with the floor. The vertical velocity 

will slow to zero for an instant at the top of the arc, and then increase in the 

DOWNWARD direction, until it reaches a maximum downward speed the instant before 

it collides with the floor. For the purpose of the following calculations, let's call the 

initial y position y 0 = 0, the top of the trajectory y top and the floor –y f . 





For the vertical direction: v 0,y = v 0 sin θ and at the top of the trajectory, v top,y = 0. 

Using the equations of motion to solve for the distance the ball travels from the 

initial y position to the top of the trajectory: 

v 

v 

2 

f 

f 

= v 

= 0 

2 

0 

− 2gy 

Calculate y, the distance from the initial launch position to the top 

of the trajectory, and write all your calculations in your lab 

notebook. 

b. This total height is the height from which the ball actually falls from rest. Add the 

height you calculated in part a to the initial height you measured for the ball in the 

launcher, tilted at an angle θ = 30 0 to get the total height. 

y total = y initial + y top = 

and write this in your notebook. 

Now calculate the time to fall this total height: 

And write it in your notebook. 

t = 

2y 

total 

g 

c. Now for the prediction: Using the total time you calculated for this predicted trajectory, 

and the horizontal component of the velocity that you calculated #2 above, calculate the 

total horizontal distance that this ball *should* travel. Show all your calculations! 

x f 

= 

v 

0 

cosθt 

And put in the expression for time above, to get a prediction. 

d. Now for the verification: Measure the distance x f that you calculated from the piece of 

tape on the floor. Make a small target with circles of 1σ, 2σ, 3σ radii, where σ is the 

distance in cm that you calculated earlier, and tape this to the floor, so that the center of 

the target is at your calculated x f . Tape a piece of carbon paper face down on top of your 

target, and SHOOT! 

e. Shoot 5 times, and then lift up the carbon paper. Did the ball hit the floor within 1σ of 

your prediction? 2σ? 3σ? Way out of the ball park? How far off your prediction did it 

hit? Put the carbon down again and, keeping everything the same, shoot 5 or 10 more 

times, and lift up the carbon. Did you come closer now? 

f. Discuss sources of errors. Would you say that the errors were systematic or random? If 

systematic, what could you do to minimize them? If random, how could you reduce the 

errors? 

4. Summary and Conclusions: Now, suppose you are called upon to present this lab 

to high school students. Write a summary of this exercise so that a high school kid 

could understand the components of projectile motion. Assume that these kids are 

sophisticated enough to know trig (sines and cosines). Suggestion: Discuss this with 

your lab partner(s). Here they should write a summary, in instruction form, of what they 





did, explaining how to find the initial velocity; when you tilt the shooter, you get x and y 

components of the initial velocity, how the ball has momentarily zero vertical velocity at 

the top, though the x-velocity continues; how the total time to fall is found from the very 

top of the trajectory; and how we're neglecting air resistance which, for this little plastic 

ball, may be more significant than for the rubber balls we used last time. 

Give +2 points for each answer; give +5 points for each graph and +5 for their 

measurements of the carbon dots and 1σ, and 95% confidence circle; give 5 points for 

each discussion of sources of errors; give +10 points for a good summary which includes 

all the points above, and is clearly written…as this tells us if they really understood what 

they were doing. Of course, these are the maximum – you can give less if the answers 

are insufficient. There is nothing really wrong…the answers will vary, and since I've 

written out most of the equations, they can't really get a wrong equation. But – they 

should write the equations in their lab notebooks, SOLVE ALL THE ALGEBRA FIRST, 

and then write their calculation or prediction. 

I did not count everything…please count the total points for all the answers, and give me 

a raw score out of the total. I'll turn it into a percentage. Please always give me raw 

scores, NOT percentages. Thanks. 

It might seem like spoon feeding…but there are a lot of beginners in this class (as 

evidenced by the number of people who came to me on Friday wanting help) and I'm a 

very classical type of teacher – practice makes perfect, especially for beginners. The 

more they practice in the presence of "experts" (you and me) the quicker they'll be able to 

do all this on their own. 

Try to get them to finish it all in lab, but if they really and truly need to finish at home, 

they can write the summary at home and bring it to class the next day (for Tuesday's lab) 

or put it in your box the following day. Writing this summary will (or, theoretically 

SHOULD) help them understand the principles of this chapter. 

Thanks!

Lab 2: Investigating Projectile Motion

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