Lesson 3C.5.2

3C.5.2 Successive oblique impacts Quiz: Pearson Edexcel Further Maths, Unit 29

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson 3C.5.2, Successive oblique impacts: 20 multiple choice questions for the Pearson Edexcel Further Maths (9FM0), Unit 29: Oblique impact, written with Revision Ninja.

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The 20 questions

  1. In successive oblique impacts of a sphere with a smooth plane, which component of velocity is constant?

    • The component parallel to the plane is reduced by e each impact
    • The component normal to the plane
    • The component parallel to the plane
    • The total speed

  2. After n successive impacts with a smooth plane, what is the normal component of velocity relative to its initial value?

    • e^(1/n) times the initial normal component
    • e n times the initial normal component
    • e^(2n) times the initial normal component
    • e^n times the initial normal component

  3. What happens to a sphere after many successive oblique impacts with a smooth plane when 0 <= e < 1?

    • The sphere reverses its parallel component
    • The sphere comes to rest completely
    • The normal component increases with each impact
    • The normal component tends to zero, and the sphere slides along the plane with constant parallel speed

  4. Which assumption is made for successive oblique impacts with a smooth plane?

    • Gravity removes the parallel component during each impact
    • No friction or air resistance acts, so the parallel component is unchanged by impact
    • Friction reduces the parallel component at each impact
    • The surface spins the sphere at each impact

  5. What assumption is made about the coefficient of restitution in successive impacts?

    • The value of e is negative
    • The same e applies at each impact
    • Each impact uses e equal to the previous speed
    • The value of e doubles at each impact

  6. For 0 <= e < 1, does the normal component of velocity tend to zero as the number of impacts becomes large?

    • Only if e = 0
    • No, it tends to e
    • No, since e^n tends to infinity
    • Yes, since e^n tends to zero

  7. Between successive impacts with a plane under gravity and no air resistance, what path does the sphere follow?

    • Simple harmonic motion
    • Uniform circular motion
    • Projectile motion, with constant horizontal velocity
    • Motion with constant acceleration in the horizontal direction

  8. A sphere has velocity (6i - 8j) m/s and strikes a smooth horizontal floor with normal along j, with e = 0.5. What is its velocity after impact?

    • -6i + 4j m/s
    • 6i - 4j m/s
    • 6i + 4j m/s
    • 3i + 4j m/s

  9. A sphere approaches a smooth horizontal floor with vertical speed 8 m/s and e = 0.5. What is its vertical speed after the second impact?

    • 0.5 m/s
    • 2 m/s
    • 4 m/s
    • 1 m/s

  10. A sphere has horizontal speed 6 m/s and strikes a smooth floor with e = 0.5. What is its horizontal speed after three impacts?

    • 3 m/s
    • 6 m/s
    • 0.75 m/s
    • 1.5 m/s

  11. A sphere has velocity (6i + 8j) and strikes a smooth horizontal plane with e = 0.5. What is its speed after three impacts, to 2 decimal places?

    • 10 m/s
    • sqrt(65) m/s
    • 6.08 m/s, from sqrt(37)
    • 6.00 m/s

  12. A sphere has velocity (6i + 8j) and strikes a smooth horizontal plane with normal along j, with e = 0.5. What angle does its velocity make with the plane after the first impact, to 1 decimal place?

    • 26.6 degrees
    • 33.7 degrees
    • 53.1 degrees
    • 45.0 degrees

  13. A sphere has velocity (6i + 8j) and strikes a smooth horizontal plane with e = 0.5. How many impacts are needed for the normal component to fall below 1% of its initial value?

    • 6
    • 5
    • 10
    • 7

  14. A sphere has velocity (6i + 8j) and strikes a smooth horizontal plane with e = 0.5. What fraction of its kinetic energy is lost in the first impact?

    • 75%
    • 52%
    • 48%
    • 25%

  15. A sphere has velocity (3i + 4j) and strikes a smooth horizontal plane with e = 0.8. What is its velocity after impact?

    • 3i - 4j
    • -3i + 3.2j
    • 2.4i - 4j
    • 3i - 3.2j

  16. A sphere has normal component 10 and parallel component 5 before impact, with e = 0.8. What is its speed after two impacts with a smooth plane, to 2 decimal places?

    • 6.40 m/s
    • 11.18 m/s
    • 8.12 m/s
    • 5.00 m/s

  17. A ball has horizontal speed 4 m/s and vertical speed 3 m/s downwards at a smooth floor, with e = 0.5 and g = 10 m/s^2. What horizontal distance does it travel between the first and second impacts?

    • 2.4 m
    • 1.5 m
    • 1.2 m
    • 0.6 m

  18. Which statement about the horizontal component during successive bounces on a smooth floor is correct?

    • It increases by a factor of e at each impact
    • It is unchanged by every impact, since the floor is smooth
    • It halves at each impact
    • It is reversed at each impact

  19. A sphere approaches a smooth floor at 45 degrees to the floor. For what coefficient e does the rebound make an angle of 30 degrees with the floor?

    • 0.866
    • 0.5
    • 0.707
    • 1/sqrt(3), about 0.577

  20. Over many oblique impacts with a smooth floor where 0 <= e < 1, which statement is best?

    • Both components tend to zero
    • The vertical component grows with each impact
    • The vertical component tends to zero while the horizontal speed remains constant
    • The horizontal component vanishes first

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