Introduction to Vectors I 21 Introduction to Vectors I 22I. Determine the horizontal and vertical components of the resultant vector by counting on

the grid.making triangle (iesame reference angle)

). This is a standard form that will allow us all to have the

X= y= O. Using your knowledge of SOH CAR TOA determine the angle between the resultant andthe horizontal. Show your work.J. Draw a mangle with horizontal and vertical components from the previous step keeping

direction of the components in mind. Determine the length of the hypotenuse usingPythagorean Theorem. Provide a scale based on the length of one block on the referencegrid.

Questions

1. How do the hypotenuse from step H and the hypotenuse for step J compare?

K. Write each of the vector pairs from the table in step E onto an individual card. Mix uporder of the cards and exchange with another group. On a piece of graph paper, diagramthe motion of the other teams toy using vector skills. Determine the resultant. Comparethe values with the other group.

2. What conclusion(s) can you draw from this finding?

3. In Step K you were not provided with any order for adding vectors. Did the randomorder have any impact on the magnitude or direction of the resultant vector?

L. Motion without a grid - Starting the ladybug from near the center of a blank dry eraseboard, allow it to move one single path to the edge of the board. The lady bug must travela path that is entirely horizontal or vertical. Trace the vector and indicate direction withan arrow. Measure the length in cm of the vector and determine the angle of the vectorrelative to the horizontal axis. Record values in the table below.

4. What is the vector term for the hypotenuse of triangle that results from combining thehorizontal and vertical vectors?

5. What type of vector quantity is represented in tltis activity?

Angle or direction ofvector relative to x axis

Conclusion (Complete in tbe space below): Compare the distance traveled to thedisplacement of the lady bug toy. Explain the difference in process for finding eachvalue. In your comparison, explain the terms vector and scalar in terms of the conceptsof distance and displacement.

Magnitude or length of Vector(cm)

Magnitude oflength of thehorizontal component (cm)

Magnitude or length of thevertical component (cm)

.-

M. On the dry erase board, draw the horizontal and vertical components of the vectorindicating appropriate direction. Measure the length of each vector and use a + or - toindicate appropriate direction on either axis. Record values in table below.

N. Draw a scaled version of the resultant displacement and the horizontal and verticalcomponents in the space provided below: [draw horizontal and then vertical when

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Introduction to Vectors I 23 Introduction to Vectors I 24~ To investigate and represent the motion of an object experiencing two simultaneous(concurrent) velocities. Vector addition and vector resolution will be used to analyze themotion of a wind-up toy.

2. Determine the resultant velocity of the toy and the paper if both have a rightwardvelocity. Attempt to move the paper at a speed similar to the toy. Fill in measurementson the table below

Wind-up ladybug3 Meter sticksDry erase gridLarge dry erase boardStop watch

Time of Displacement Displacement Displacement Velocity Velocity ResultantInterval of paper of ladybug ofthe ofthe ofthe velocity

relative to relative to ladybug paper ladybug ofthemeter stick the grid relative to on the ladybug

the meter papersticks(resultant)

Procedure:A. Motion of the toy is due to wind up device. Before all experiments the toy will be fully

wound.B. The paper moves along the horizontal x axis by pulling it at roughly constant speedC. The relative motion of the objects is found by moving both the paper and the toy

between stationary meter sticks

Prior to all data collection students should practice coordinating materials and establish arealistic division of labor. See your instructor if you need assistance with this step

a) Show your work used to determine the velocity values for the chart above

1. Determine the average speed of the ladybug as it moves toward the right across astationary grid. (Take the average of 3 trials). You will use this average speed as areference value throughout the lab.

b) Construct a vector diagram that shows how the displacement of the toy and thedisplacement of the paper add to the resultant displacement of the toy. (Label eachvector with a magnitude Including units. Does not have to be drawn to scale butshould show relative size.)

Data and Calculations

Toy DataDistance (cm) TIme Speed

AVERAGE

c) Construct a vector diagram that shows how the velocity of the toy and the velocityof the paper add to the resultant velocity of the toy. (Label each vector with amagnitude including units. Does not have to be drawn to scale but should showrelative size.)

d) Since the paper and the lady bug are both moving in the same direction, how wouldwe define the angle between their motions?

Introduction to Vectors I 25 Introduction to vectors! 26

3. Move the paper to the left at a similar constant speed to that of the rightward movinglady bug for several seconds. As a group record the following. Note the direction ofmotion with a positive or negative sign.

Time of Horizontal Vertical Displacement Velocity Velocity Resultantexperiment Displacement Displacement olthe ofthe of the velocity of

of paper of ladybug ladybug paper ladybug therelative to relative to relative to onthe ladybugmeter stick the grid the meter paper

sticks(resultant)

.Magnitude: Magnitude:

Angle: Angle:

Time of Displacement Displacement Displacement Velocity Velocity Resultantexperiment of paper of ladybug olthe of the of the velocity

relative to relative to ladybug paper ladybug of themeter stick the grid relative to on the ladybug

the meter papersticks(resultant)

b) Construct a labeled velocity diagram ... , 1*'1 cr

Construct displacement and velocity vector diagrams showing components andresultants.

6. Predict what would happen to the angle of motion if you pull the paper at twice thespeed to the right while the lady bug moves upward. Roughly draw the vectors (Hint:think of the paper as the x vector and the toy as the y vector)

7. Complete the scenario presented in the previous question. (ie lady bug upward andpaper 2X velocity right)

a) Construct a labeled displacement diagram 'if I'ot

c) What is the difference in direction (angle) between the papers velocity and theladybugs velocity?

S. With the toy starting at the bottom left corner of the paper and pointed upward, pullthe paper to the right at a pace close to that of the toy. Let it run until the toy reaches apoint at the top. On the dry erase board, draw a line that connects the start and endpoint (ie, the resultant displacement) Fill in data on the chart below

Time of Horizontal Vertical Displacement Velocity Velocity Resultantexperiment Displacement Displacement of the of the of the velocity of

of paper of ladybug ladybug paper ladybug therelative to relative to relative to onthe ladybugmeter stick the grid the meter paper

sticks(resultant)

Magnitude: Magnitude:

Angle: Angle:

4. Vector Rule: The maximum resultant occurs when the vectors are arranged at an angleof or similar direction. The minimum resultant occurs when the vectorsare arranged at an angle of or opposite direction. How could you geta different resultant without changing the magnitude (size) of the component velocityvectors?

)r~ 1- ,.J7~ a. Draw a labeled vector diagram of the resultant displacement and horizontal and

vertical components.b. Determine the resultant velocity (magnitude and direction). Show work

Introduction to Vectors I 27 Introduction to Vectors I 28

13. When an object is launched at an angle, the initial or start velocity can be broken downinto two components, velocity directed horizontally and velocity directed vertically.What is the launch velocity of an object with a horizontal component of 40 m/s and avertical component of 30 m/s?

8. Predict what would happen to the angle of motion if the velocity of the paper weremoving to the right at a velocity about half that of the lady bug. Draw the predictedvector diagram. Complete this scenario with the materials. Does the actual motionmatch)l'61lrediction?rvr

9. Draw the observed resultant path (and components) for the lady bug moving upward~aper moving to the left (use similar speeds for both the paper and the~ Labe.!.!becprnpo~ with the appropriate sign (+ or -I.

14. What are the initial horizontal and vertical components of an object's velocity if it islaunched at 35 m/s at an angle of 60 degrees?

Conclusions; (to be completed on a separate paper and attached) •

ing rightward. (UkC , 1fI. ..-f;, ,,~

'omponents) for the lady bug starting from the /

while the paper is moving leftward a/t Fy,

12. a) Determine the horizontal component of the motion of the paper if t~travelled with a resultant speed of 14.2 m/s and a vertical speed of 8 m~ourwork.

J

Explain how the addition of vector quantities is different from addition of scalarquantities. Differentiate between the terms speed and velocity. Explain why vectors arean important concept in motion and how they can be useful in other aspects of physics(Think about real life scenarios in which this applies). Summarize the methods ofcombining horizontal motion and vertical motion to determine a resultant and themethods for finding the horizontal and vertical components of a resultant vector.Explain how the angle between the vectors influences the magnitude of the resultantvector. Be sure to define terms used in your explanations.

Hint: V= Vy=

b) What was the angle of the resultant for the previous problem if the lady bug wasmoving upward and the paper was moving left? (show work with equation andsubstitution)

c) What will be the resultant displacement of the lady bug after 4 seconds? Show work(include magnitude and directions)

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