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Solutions to Vector Components Worksheet, Exercises of Chemistry

Baldwin Wallace University (BW)Chemistry

Physics 1C topic exercise questions and answers on vector components

Typology: Exercises

2020/2021
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Solutions to Physics I C Vector Components Worksheet
Vector Components Worksheet
1. Using dotted lines, draw the horizontal and vertical components for each vector shown below. Show only one
pair of the components.
2. Using the angles given on the diagrams in problem #1 above, calculate the values of the horizontal ( x ) and
vertical ( y ) components for each diagram you did above, showing your work in the box for each below.
Note: Be sure your calculator is in “DEGREE” mode before doing your calculations.
X = Y =
𝐴𝑥=𝐴cos𝜃 = 40 𝑚 cos140°
=−30.6 𝑚
𝐴𝑦= 𝐴sin𝜃 = 40 𝑚 sin140°
=25.7 𝑚
X = Y =
𝐴𝑥=𝐴cos𝜃 = 9 𝑙𝑏cos20°
=8.46 𝑙𝑏
𝐴𝑦= 𝐴 sin 𝜃 = 9 𝑙𝑏sin20°
=3.08 𝑙𝑏
X = Y =
𝐴𝑥=𝐴cos𝜃 = 20 𝑘𝑚 cos255°
=−5.18 𝑘𝑚
𝐴𝑦= 𝐴sin𝜃 = 20 𝑘𝑚sin255°
=−19.32 𝑘𝑚
X = Y =
𝐴𝑥=𝐴cos𝜃 = 15 𝑚 𝑠
⁄cos320°
=11.5 𝑚 𝑠
⁄
𝐴𝑦= 𝐴sin𝜃 = 15𝑚 𝑠
⁄sin320°
=−9.64 𝑚 𝑠
⁄
X = Y =
𝐴𝑥=𝐴cos𝜃 = 45 𝑁 cos200°
=−42.3 𝑁 𝑙𝑏
𝐴𝑦= 𝐴sin𝜃 = 45 𝑁 sin 200°
=−15.4 𝑁
X = Y =
𝐴𝑥=𝐴cos𝜃 = 15 𝑓𝑡 cos80°
= 2.6 𝑓𝑡
𝐴𝑦= 𝐴sin 𝜃 = 15 𝑓𝑡 sin80°
=14.8 𝑓𝑡 𝑙𝑏
X = Y =
𝐴𝑥=𝐴cos𝜃 = 6 𝑚𝑖cos270° =0
𝐴𝑦= 𝐴 sin 𝜃 = 6 𝑚𝑖sin270°
= 6 𝑚𝑖
X = Y =
𝐴𝑥=𝐴cos𝜃 = 50 𝑚 𝑠2
⁄cos0°
=50 𝑚 𝑠2
⁄
𝐴𝑦= 𝐴sin 𝜃 = 50 𝑚 𝑠2
⁄sin0°
=0
X = Y =
𝐴𝑥=𝐴cos𝜃100𝑚 𝑠
⁄cos330°
=86.8 𝑚 𝑠
⁄
𝐴𝑦=𝐴sin𝜃100𝑚 𝑠
⁄sin330°
=−50 𝑚 𝑠
⁄
40 m, 40o from horizontal
9 lb, 20o from hroizontal
20 km 15o from vertical
15 m/s, 50o from vertical
45N, 70o from vertical
15 ft, 80o from horizontal
50 m/s2, 0o from horizontal
100 m/s, 30o from horizontal
Ax
Ax
Ax
Ax
Ax
Ay
Ay
Ay
Ay
Ay
Ay
Ay
Ay
Ax
Ax
pf3
pf4
pf5
Discount

On special offer

Partial preview of the text

Download Solutions to Vector Components Worksheet and more Exercises Chemistry in PDF only on Docsity!

Solutions to Physics I C Vector Components Worksheet

Vector Components Worksheet

  1. Using dotted lines, draw the horizontal and vertical components for each vector shown below. Show only one pair of the components.
  2. Using the angles given on the diagrams in problem #1 above, calculate the values of the horizontal ( x ) and vertical ( y ) components for each diagram you did above, showing your work in the box for each below. Note: Be sure your calculator is in “DEGREE” mode before doing your calculations.

X = Y = 𝐴𝑥 = 𝐴 cos 𝜃 = 40 𝑚 cos 140° = − 30. 6 𝑚 𝐴𝑦 = 𝐴 sin 𝜃 = 40 𝑚 sin 140° = 25. 7 𝑚

X = Y =

𝐴𝑥 = 𝐴 cos 𝜃 = 9 𝑙𝑏 cos 20° = 8. 46 𝑙𝑏 𝐴𝑦 = 𝐴 sin 𝜃 = 9 𝑙𝑏 sin 20° = 3. 08 𝑙𝑏

X = Y =

𝐴𝑥 = 𝐴 cos 𝜃 = 20 𝑘𝑚 cos 255° = − 5. 18 𝑘𝑚 𝐴𝑦 = 𝐴 sin 𝜃 = 20 𝑘𝑚 sin 255° = − 19. 32 𝑘𝑚 X = Y = 𝐴𝑥 = 𝐴 cos 𝜃 = 15 𝑚 ⁄𝑠 cos 320° = 11. 5 𝑚 ⁄𝑠 𝐴𝑦 = 𝐴 sin 𝜃 = 15 𝑚 ⁄𝑠 sin 320° = − 9. 64 𝑚 ⁄𝑠

X = Y =

𝐴𝑥 = 𝐴 cos 𝜃 = 45 𝑁 cos 200° = − 42. 3 𝑁 𝑙𝑏 𝐴𝑦 = 𝐴 sin 𝜃 = 45 𝑁 sin 200° = − 15. 4 𝑁

X = Y =

𝐴𝑥 = 𝐴 cos 𝜃 = 15 𝑓𝑡 cos 80° = 2. 6 𝑓𝑡 𝐴𝑦 = 𝐴 sin 𝜃 = 15 𝑓𝑡 sin 80° = 14. 8 𝑓𝑡 𝑙𝑏 X = Y = 𝐴𝑥 = 𝐴 cos 𝜃 = 6 𝑚𝑖 cos 270° = 0 𝐴𝑦 = 𝐴 sin 𝜃 = 6 𝑚𝑖 sin 270° = 6 𝑚𝑖

X = Y =

𝐴𝑥 = 𝐴 cos 𝜃 = 50 𝑚 ⁄𝑠 2 cos 0° = 50 𝑚 ⁄𝑠^2 𝐴𝑦 = 𝐴 sin 𝜃 = 50 𝑚 ⁄𝑠^2 sin 0° = 0

X = Y =

𝐴𝑥 = 𝐴 cos 𝜃 100 𝑚 ⁄𝑠 cos 330° = 86. 8 𝑚 ⁄𝑠 𝐴𝑦 = 𝐴 sin 𝜃 100 𝑚 ⁄𝑠 sin 330° = − 50 𝑚 ⁄𝑠

40 m, 40o^ from horizontal 9 lb, 20o^ from hroizontal 20 km 15o^ from vertical

15 m/s, 50o^ from vertical 45N, 70o^ from vertical 15 ft, 80o^ from horizontal

6 mi, 0o^ from vertical 50 m/s^2 , 0o^ from horizontal 100 m/s, 30o^ from horizontal

Ax

Ax

Ax^ Ax

Ax

Ay^ Ay

Ay

Ay Ay

Ay

Ay

Ay

Ax

Ax

  1. A dodge ball player is trying to avoid getting hit by the opposing team. The player runs 2.7 m at an angle 37o They then run 4.9 m at an angle of 62o^. Then then runs 1.7 m at an angle of 13o^.

a. Draw the x and y components of the b. Calculate the resultant displacement. individual vectors on the diagram below.

𝐴𝑥 = 𝐴 cos 𝜃 = 2.7 𝑚 cos 37° = 2.16 𝑚 𝐴𝑦 = 𝐴 sin 𝜃 = 2.7 𝑚 sin 37° = 1.62 𝑚

𝐵𝑥 = 𝐵 cos 𝜃 = 4.9 𝑚 cos 62° = 2.30 𝑚 𝐵𝑦 = 𝐵 sin 𝜃 = 4.9 𝑚 sin 62° = 4.33 𝑚

𝐶𝑥 = 𝐶 cos 𝜃 = 1.7 𝑚 cos 13° = 1.65 𝑚 𝐶𝑦 = 𝐶 sin 𝜃 = 1.7 𝑚 sin 13° = 0.38 𝑚

𝑅𝑥 = 𝐴𝑥 + 𝐵𝑥 + 𝐶𝑥 = 2.16 𝑚 + 2.30 𝑚 + 1.65 𝑚 = 6.11 𝑚 𝑅𝑦 = 𝐴𝑦 + 𝐵𝑦 + 𝐶𝑦 = 1.62 𝑚 + 4.33 𝑚 + 0.38 𝑚 = 6.33 𝑚

𝑅 = √𝑅𝑥^2 + 𝑅𝑦^2 = √(6.11 𝑚)^2 + (6.33 𝑚)^2 = 8.80 𝑚

𝜃 = tan−1^ (

𝑅𝑥^ ) = tan

Vector A

Ax Ay

Vector B

Bx By

Vector C

Cx Cy

  1. A rocket hits the ground at an angle of 60o^ from the horizontal at a speed of 300 m/s. a. Draw the vector representing the b. Calculate the horizontal and vertical components rocket’s impact and show the westward of the rocket’s impact velocity. and eastward components of it’s velocity.

𝐴𝑥 = 𝐴 cos 𝜃 = 300 𝑚 𝑠⁄ cos 60° = 150 𝑚 𝑠⁄ ℎ𝑜𝑟𝑖𝑧𝑜𝑛𝑡𝑎𝑙 𝐴𝑦 = 𝐴 sin 𝜃 = 300 𝑚 𝑠⁄ sin 60° = 259.8 𝑚 𝑠⁄ 𝑣𝑒𝑟𝑡𝑖𝑐𝑎𝑙

Ay

Ax

A squirrel runs out into the street in front of your car. The squirrel runs at an angle of 39o^ for 3.0 m, turns around and runs 5.5 m at an angle of 51o^. a. Draw the individual vectors. b. Calculate the resultant vector.

𝐴𝑥 = 𝐴 cos 𝜃 = 3.0 𝑚 cos 39° = 2.33 𝑚 𝐴𝑦 = 𝐴 sin 𝜃 = 3.0 𝑚 sin 39° = 1.89 𝑚

𝐵𝑥 = 𝐵 cos 𝜃 = 5.5 𝑚 cos 51° = 3.46 𝑚 𝐵𝑦 = 𝐵 sin 𝜃 = 5.5 𝑚 sin 51° = 4.27 𝑚

𝑅𝑥 = 𝐴𝑥 + 𝐵𝑥 = 2.33 𝑚 + 3.46 𝑚 = 5.79 𝑚 𝑅𝑦 = 𝐴𝑦 + 𝐵𝑦 = 1.89 𝑚 + 4.27 = 6.16 𝑚

𝑅 = √𝑅𝑥^2 + 𝑅𝑦^2 = √(5.79 𝑚)^2 + (6.16 𝑚)^2 = 8.45 𝑚

𝜃 = tan−1^ (

𝑅𝑥^ ) = tan

Vector A

Ax Ay

Vector B

Bx By