Unit vectors, vector sums and combinations

Answer Key - Grade 11 Math Worksheet - Challenge Me

Circle the best answer, or write your answer on the line.

1. 1.

   Two friends pull a sled: one with 10 N at 0°, the other with 10 N at 60°, angles from east. Ren adds them. To the nearest tenth, how large is the total?

   17.3
2. 2.

   A plane flies at 12 km/h at 30°, and the wind adds 5 km/h at 120°, angles from east. Tala adds them. To the nearest tenth, how large is the total?

   13
3. 3.

   Two ropes pull a boat: one with 20 N at 30°, the other with 15 N at 120°, angles from east. Zee adds them. To the nearest tenth, how large is the total?

   25
4. 4.

   Two kids pull a wagon: one with 6 N at 0°, the other with 10 N at 120°, angles from east. Esme adds them. To the nearest tenth, how large is the total?

   8.7
5. 5.

   A game piece has two jumps, u = ⟨2, 1⟩ and v = ⟨1, 3⟩. Luz wants a·u + b·v = ⟨8, 9⟩. Written as (a, b), what are the two numbers?

   (3, 2)
6. 6.

   A crane has two arm moves, u = ⟨3, 2⟩ and v = ⟨-1, 1⟩. Noah wants a·u + b·v = ⟨2, 8⟩. Written as (a, b), what are the two numbers?

   (2, 4)
7. 7.

   Two ropes pull a sled with F₁ = ⟨30, 40⟩ N and F₂ = ⟨50, -10⟩ N. Pia adds a third pull F₃ so nothing moves. As (run, rise), what is F₃?

   (-80, -30)
8. 8.

   Two kids pull a wagon with F₁ = ⟨-20, 35⟩ N and F₂ = ⟨60, 15⟩ N. Ren adds a third pull F₃ so nothing moves. As (run, rise), what is F₃?

   (-40, -50)
9. 9.

   Two ropes hold a boat with F₁ = ⟨45, -25⟩ N and F₂ = ⟨-15, -30⟩ N. Tala adds a third pull F₃ so nothing moves. As (run, rise), what is F₃?

   (-30, 55)
10. 10.

    Two cables pull a box with F₁ = ⟨-40, -10⟩ N and F₂ = ⟨-25, 55⟩ N. Zee adds a third pull F₃ so nothing moves. As (run, rise), what is F₃?

    (65, -45)