Lesson E9

E9 Trigonometry in context: vectors, kinematics and forces Quiz: AQA Maths, Unit 5

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson E9, Trigonometry in context: vectors, kinematics and forces: 20 multiple choice questions for the AQA Maths (7357), Unit 5: Trigonometry, written with Revision Ninja.

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The 20 questions

  1. A vector of magnitude 10 makes an angle of 60 degrees with the x-axis. What is its x-component?

    • 10 sqrt(3)
    • 5
    • 5 sqrt(3)
    • 10

  2. A force of 20 N acts at 30 degrees to the horizontal. What is its horizontal component?

    • 20 sqrt(3) N
    • 10 N
    • 10 sqrt(3) N
    • 20 N

  3. Two forces of 3 N and 4 N act with an angle of 60 degrees between them. What is the magnitude of the resultant?

    • sqrt(13) N
    • 5 N
    • sqrt(37) N
    • 7 N

  4. To the nearest degree, what angle does the vector (3, 4) make with the positive x-axis?

    • 45 degrees
    • 53 degrees
    • 63 degrees
    • 37 degrees

  5. A projectile is launched at angle theta with speed u. Which expression gives its horizontal velocity component?

    • u cos theta
    • u cos^2 theta
    • u sin theta
    • u tan theta

  6. A projectile is launched with speed 20 m/s at 30 degrees. What is its initial vertical velocity?

    • 10 sqrt(3) m/s
    • 20 sqrt(3) m/s
    • 20 m/s
    • 10 m/s

  7. Which formula gives the range of a projectile launched from level ground with speed u at angle theta, with no air resistance?

    • R = u^2 sin theta / g
    • R = u^2 cos 2 theta / g
    • R = u^2 sin 2 theta / g
    • R = 2u sin theta / g

  8. A projectile is launched from level ground at 20 m/s and 30 degrees, with g = 9.8 m/s^2. What is its range?

    • 35.3 m
    • 70.6 m
    • 17.7 m
    • 40.8 m

  9. A projectile is launched at 20 m/s and 30 degrees, with g = 9.8 m/s^2. What is its maximum height?

    • 10.2 m
    • 2.55 m
    • 20.4 m
    • 5.10 m

  10. A 2 kg particle rests on a smooth slope at 30 degrees, with g = 10 m/s^2. What is the component of its weight acting down the slope?

    • 17.3 N
    • 10 N
    • 5 N
    • 20 N

  11. A 5 kg block rests on a smooth plane inclined at 40 degrees, with g = 9.8 m/s^2. What is the normal reaction?

    • 31.5 N
    • 49.0 N
    • 24.5 N
    • 37.5 N

  12. Which equation links displacement s, initial velocity u, final velocity v and time t, without acceleration?

    • s = (u + v) t / 2
    • s = ut + v^2
    • s = (u - v) t / 2
    • s = (u + v) / (2t)

  13. A ladder of length 5 m makes an angle of 60 degrees with the horizontal floor. How high does it reach up the wall?

    • 5 m
    • 2.5 m
    • 4.33 m
    • 8.66 m

  14. What is the unit vector in the direction of (3, 4)?

    • (0.5, 0.5)
    • (3, 4)
    • (0.6, 0.8)
    • (0.8, 0.6)

  15. A boat moves at 4 m/s due north in a current of 3 m/s due east. To the nearest degree, what angle east of north is its resultant velocity?

    • 53 degrees
    • 45 degrees
    • 31 degrees
    • 37 degrees

  16. A 10 N weight is held by two equal strings, each at 30 degrees to the horizontal. What is the tension in each string?

    • 20 N
    • 10 sqrt(3) N
    • 10 N
    • 5 N

  17. Forces of (3, 4) and (-1, 2) act on a particle. What is the magnitude of the resultant force?

    • sqrt(52)
    • 2 sqrt(10)
    • sqrt(26)
    • 8

  18. A projectile is launched from level ground at 20 m/s and 30 degrees, with g = 10 m/s^2. What is its time of flight?

    • 2 s
    • 1 s
    • 4 s
    • 3.46 s

  19. Vectors a and b have magnitudes 3 and 5, with angle 60 degrees between them. What is the magnitude of a - b?

    • sqrt(19)
    • sqrt(7)
    • sqrt(34)
    • sqrt(49)

  20. A particle has velocity (3t, 4) m/s. What is its speed at t = 2 s?

    • 6 m/s
    • 10 m/s
    • sqrt(34) m/s
    • 2 sqrt(13) m/s

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