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

The 20 questions

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

   • Vertical component
   • Normal component
   • Parallel component
   • Resultant speed

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

   • n times e initial
   • e times initial
   • initial divided by n
   • e^n times initial

3. What happens to a sphere's normal velocity component after many successive oblique impacts when 0 <= e < 1?

   • Oscillates
   • Remains constant
   • Tends to infinity
   • Tends to zero

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

   • Maximum friction
   • Zero friction
   • Constant friction
   • Variable friction

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

   • Zero e
   • Constant e
   • Increasing e
   • Decreasing e

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

   • Depends on mass
   • Depends on angle
   • No
   • Yes

7. Between successive impacts with a plane under gravity, what path does the sphere follow?

   • Straight line
   • Circular motion
   • Projectile motion
   • Simple harmonic motion

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. What happens to the horizontal velocity component during successive bounces on a smooth floor?

    • It becomes zero
    • It is unchanged
    • It decreases by e
    • It increases

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, what happens to the vertical speed?

    • Remains constant
    • Fluctuates
    • Tends to zero
    • Increases

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