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CAIE A-Level Physics Geometry, Trigonometry and Vectors

Practise choosing areas, volumes, Pythagoras, trigonometry, vector addition or perpendicular resolution before applying the relevant physics equation.

Syllabus
2028–2030
Course
Physics 9702
Level
AS

Exam points

  • use areas and volumes, including unit conversions, to calculate physical quantities
  • apply Pythagoras, similar triangles and trigonometric relationships to physical diagrams
  • resolve or combine vectors into perpendicular components in a physical context

M.3-Geometry, trigonometry and vectors question 1

[Maximum number: 1]

A pendulum consists of a solid sphere suspended by a string from a fixed point P , as shown in Fig. 3.1.

Fig. 3.1 (not to scale)

Fig. 3.1 (not to scale)

The sphere swings from side to side. At one instant the sphere is at its lowest position X , where it has kinetic energy 0.86 J and momentum 0.72 Ns in a horizontal direction. A short time later the sphere is at position Y , where it is momentarily stationary at a maximum vertical height h above position X.

The string has a fixed length and negligible weight. Air resistance is also negligible.

The distance between point P and the centre of the sphere is 0.93 m . When the sphere is at position Y , the string is at an angle θ\theta to the vertical.

Show that θ\theta is 47∘47^{\circ}.

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