Lesson 3C.4.2

3C.4.2 Successive direct impacts Quiz: Pearson Edexcel Further Maths, Unit 28

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson 3C.4.2, Successive direct impacts: 20 multiple choice questions for the Pearson Edexcel Further Maths (9FM0), Unit 28: Direct impact, written with Revision Ninja.

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The 20 questions

  1. A sphere hits a fixed smooth vertical wall perpendicularly at speed u with coefficient of restitution e. What is its speed after impact?

    • e u
    • e^2 u
    • u / e
    • u (1 - e)

  2. A ball is dropped from height h onto a fixed horizontal smooth plane with coefficient e. What is the height of its first rebound?

    • h / e^2
    • e^2 h
    • e h
    • (1 - e) h

  3. What pattern do the speeds after successive impacts with a fixed smooth plane follow?

    • A geometric sequence with common ratio e
    • An arithmetic sequence with common difference e
    • All speeds are equal
    • A geometric sequence with common ratio e^2

  4. What is the sum to infinity of a geometric series with first term a and common ratio r, |r| < 1?

    • a (1 - r)
    • a / (1 - r)
    • a (1 + r)
    • a r / (1 - r)

  5. Why do successive impacts of a sphere with a fixed plane eventually stop for e < 1?

    • The sphere loses mass at each impact
    • Momentum is created at each impact
    • Gravity increases with each bounce
    • Each impact multiplies the speed by e, which is less than 1, so the speeds tend to zero

  6. What happens to successive bounces of a sphere when e = 1 on a smooth fixed plane?

    • The sphere stops after the first bounce
    • The speed doubles at each bounce
    • The bounces continue indefinitely with the same speed
    • The speed halves at each bounce

  7. A sphere leaves a smooth horizontal plane vertically upwards at speed v, under gravity g. How long does it take to return to the plane?

    • v/g
    • v^2/(2g)
    • 2v/g
    • 2g/v

  8. A sphere is dropped from a height of 4 m onto a smooth horizontal plane with e = 0.5. How high does it rebound?

    • 2 m
    • 4 m
    • 0.5 m
    • 1 m

  9. A sphere is dropped from a height of 4 m onto a smooth horizontal plane with e = 0.5 and g = 9.8. What is its speed just after the first impact, to 2 decimal places?

    • 2.21 m/s
    • 4.43 m/s
    • 8.85 m/s
    • 4.00 m/s

  10. A sphere strikes a fixed smooth plane with speed 10 m/s with e = 0.6. What is its speed after the second impact?

    • 2.16 m/s
    • 1.2 m/s
    • 3.6 m/s
    • 6.0 m/s

  11. A ball is dropped from a height of 2 m onto a smooth horizontal floor with e = 0.5. What is the total distance it travels before the bounces stop, to 2 decimal places?

    • 4.00 m
    • 2.67 m
    • 6.00 m
    • 3.33 m

  12. A sphere bounces off a fixed smooth wall with e = 0.75 after successive impacts, having approach speed 8 m/s. What is its speed after the second impact?

    • 4.5 m/s
    • 3.0 m/s
    • 2.25 m/s
    • 6 m/s

  13. A ball leaves a horizontal floor vertically upwards at 6 m/s, with g = 10 m/s^2. How long until it returns to the floor?

    • 3.6 s
    • 0.6 s
    • 1.2 s
    • 6 s

  14. A sphere is dropped from a height of 10 m onto a smooth plane with e = 0.8. What is its height after the third rebound, to 2 decimal places?

    • 5.12 m
    • 2.62 m
    • 8.00 m
    • 1.60 m

  15. A sphere has speed 20 m/s and e = 0.5 on repeated impacts with a smooth fixed plane. What is its speed after four impacts?

    • 0.625 m/s
    • 1.25 m/s
    • 10 m/s
    • 2.5 m/s

  16. A ball is dropped from rest from a height of 1.8 m with e = 0.6. What is its height after the second bounce, to 3 decimal places?

    • 0.389 m
    • 0.648 m
    • 0.233 m
    • 1.080 m

  17. A ball is dropped from rest from a height of 1 m onto a smooth horizontal floor with e = 0.5 and g = 10 m/s^2. What is the total time until the bounces stop, to 2 decimal places?

    • 2.24 s
    • 0.89 s
    • 1.34 s
    • 0.45 s

  18. For successive impacts of a sphere on a smooth fixed plane, what fraction of the kinetic energy is lost at each impact?

    • 1 - 2e
    • 1 - e^2
    • e^2
    • 1 - e

  19. A sphere has speed 9 m/s before ten successive impacts with a smooth fixed plane with e = 0.9. What is its speed after the tenth impact, to 2 decimal places?

    • 0.35 m/s
    • 3.49 m/s
    • 4.05 m/s
    • 3.14 m/s

  20. Why does the total time for successive bounces converge when e < 1?

    • The flight times form a geometric series with common ratio e, which is less than 1, so the sum is finite
    • Because e equals one half in every case
    • Each bounce takes exactly the same time
    • Gravity is constant, so the sum of the times is always finite

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