2016 Calculus Physics

AP Chapter 3 Practice WorksheetName____________________

Hour_____Score___/ 101 pts

1. (2pts) In 1969 three Apollo astronauts left Cape Canaveral, went to the Moon and back, and splashed down in the Pacific Ocean. An admiral bid them good-bye at the Cape and then sailed to the Pacific Ocean in an aircraft carrier where he picked them up. Compare the displacements of the astronauts and the admiral.

2. (2pts)Three displacements are A = 200 m, due north; B = 250 m, due east; C = 150 m, 30° east of south. Add the vectors graphically (draw it… answers are pictures not numbers) for each of the following orders: See https://phet.colorado.edu/en/simulation/legacy/vector-addition for help.

R1 = A + B + C R2 = B + C + A R3 = C + B + A

3. What are the x and y components of a vector a in the xy plane if its direction is 2300 counter- clockwise from the positive direction of the x axis and its magnitude is 7.3 m? (2pts)

2016 Calculus Physics

4. Vector a has a magnitude of 5 m and is directed east. Vector b has a magnitude of 3 m and is directed 115 degrees from the positive x axis. See flowchart at : http://zonalandeducation.com/mstm/physics/mechanics/vectors/componentAddition/componentAddition2.htm for help. a. (2pts)What is the magnitude and direction of a + b?

b. (2pts)What is the magnitude and direction of b-a?

5. For the vectors a= (7.0m)i + (3.0m)j and b=(5.0 m)i + (-2.0m)j, Find a+ba. (2pts)Unit-vector notation

b. (2pts)magnitude and angle

find a-bc. (2pts)unit-vector notation

d. (2pts)magnitude and angle

2016 Calculus Physics

6. You are to make four straight-line moves over a flat desert floor, starting at the origin of an xy coordinate system and ending at the xy coordinates (-120 m, 40 m). The x component and y component of your moves are the following, respectively, in meters: (30, 50), then (bx, and -50), then (-15 and cy), then (-60 and -70).What are (a) component bx and (b) component cy? What are (c) the magnitude and (d) the angle (relative to the positive direction of the x axis) of the overall displacement? (8pts)

7. (a) What is the sum of the following four vectors in unit- vector notation? For that sum, what are (b) the magnitude, (c) the angle in degrees, (6pts)

E: 6 m at 45.90 F: 4 m at -750

G : 5m at 80.250 H : 3 m at -2200

2016 Calculus Physics

8. Here are two vectors:a=(3m ) i+(5m) j b=(7m ) i−(8m) j

a. (2pts) What is the angle between a and b?

b. (2pts)What is magnitude and angle of a+b?

c. (2pts)What is the magnitude and angle of b-a?

d. (2pts)What is the magnitude and angle of a-b?

e. (2pts)What is the angle between the last two answers above (part c and d)? What does this tell you about vector subtraction?

9. (2pts) If a−b=2 c , a+ b=4 c ,∧ c=6 i+8 j, then what are a ,∧b?

2016 Calculus Physics

10. (2pts)Find the angle between a=3 i+2 j+6 k and b=2 i+1 j+3 k

11. Remember PEMDASThree vectors are given by:

[ ] units are meters for all vectors and all components.

a. (2pts)Find a ° (b× c)

2016 Calculus Physics

b. (2pts)Find a °(b+c)

Three vectors are given by:

[ . ]All vectors and components have the unit of meters

c. (2pts)Find a×(b−c )

d. (2pts)Find 3 c °( a×2 b)

2016 Calculus Physics

e. (2pts) Find the angle between vector b and vector c.

12. (2pts)You know F=q v× B where q=2 C, F=4 N i−20N j+12N k and v=2m /s i+4m /s j+6m /s k . Find the magnetic field (B)in unit-vector notation if Bx=By.

2016 Calculus Physics

0 1 2 3 4 5 6 7 8 9 10 110

2

4

6

8

Position versus time graph

time(s)

Posi

tion

(m)

0 1 2 3 4 5 6 7 8 9 10 11

-3-2-10123

Velocity versus time graph

time(s)

velc

otiy

(m/s

)

13. a. Fill in the information below for the position vs time graph above (1 pt each)

0-2 seconds 2-4 seconds 4-7 seconds 7-10 seconds

In what direction is the object moving?

(Right/left/both/not moving)

What is the velocity of the object?

(number with unit)

Leave this box blank

Is the object at rest, speeding up, slowing down, traveling at a constant velocity?

Is there an acceleration?

(yes or no)

b. (2pts)Find the average velocity from 2 seconds to 9 seconds.

c. (2pts)Find the instantaneous velocity at 9 seconds.

d. (2pts) Fill in the corresponding velocity vs time graph (located to the right of the position vs time graph) with the information from your chart.

2016 Calculus Physics

14.

Fill in the information below (1pt each box)

0-6 seconds 6-8 seconds 8-10 seconds

What direction is the object moving in? (right or left or both or not moving)

Calculate the acceleration of the object.

Is the object speeding up or slowing down or both or at rest or traveling at a constant velocity?

What is the displacement of the object for the time interval?

a. (2pts)Find the average acceleration from 2 seconds to 7 seconds.

b. (2pts) Draw the corresponding position vs time graph using the information in your chart. Assume the object starts at the origin.

0 1 2 3 4 5 6 7 8 9 10 11

-6

-4

-2

0

24

velocity versus time graph

time (s)

velo

city

(m/s

)

0 1 2 3 4 5 6 7 8 9 10 11

-10

-5

0

5

10

position versus time graph

time (s)

posi

tion

(m)

2016 Calculus Physics

15. (a) (2pts)On the axes below, plot the data points for velocity as a function of time for the glider, and draw a smooth curve that best fits the data. Be sure to label an appropriate scale on the vertical axis.

(b) (2pts)The student wishes to use the data to plot position x as a function of time t for the glider.

i. Describe a method the student could use to do this. (a sentence or two is sufficient, this is asking you to describe in words what you are using from the above graph to draw your position vs time graph)

ii. (2pts) On the axes to the right, sketch the position x as a function of time t for the glider. Explicitly label any intercepts, asymptotes, maxima, or minima with numerical values or algebraic expressions, as appropriate.