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Physics 1C topic exercise questions and answers on vector components
Typology: Exercises
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Solutions to Physics I C Vector Components Worksheet
Vector Components Worksheet
X = Y = 𝐴𝑥 = 𝐴 cos 𝜃 = 40 𝑚 cos 140° = − 30. 6 𝑚 𝐴𝑦 = 𝐴 sin 𝜃 = 40 𝑚 sin 140° = 25. 7 𝑚
𝐴𝑥 = 𝐴 cos 𝜃 = 9 𝑙𝑏 cos 20° = 8. 46 𝑙𝑏 𝐴𝑦 = 𝐴 sin 𝜃 = 9 𝑙𝑏 sin 20° = 3. 08 𝑙𝑏
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
𝐴𝑥 = 𝐴 cos 𝜃 = 45 𝑁 cos 200° = − 42. 3 𝑁 𝑙𝑏 𝐴𝑦 = 𝐴 sin 𝜃 = 45 𝑁 sin 200° = − 15. 4 𝑁
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
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
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
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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
𝜃 = tan−1^ (
𝑅𝑥^ ) = tan
Vector A
Ax Ay
Vector B
Bx By
Vector C
Cx Cy
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
𝜃 = tan−1^ (
𝑅𝑥^ ) = tan
Vector A
Ax Ay
Vector B
Bx By