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CAIE A-Level Physics 1.4.3 Perpendicular Vector Components

Practise resolving force, weight or velocity vectors into perpendicular components, using trigonometry and recombining them in the stated coordinates.

Syllabus
2028–2030
Course
Physics 9702
Level
AS

Exam points

  • Resolve a vector into two perpendicular components along chosen axes.
  • Use trigonometry or components to calculate the magnitude and direction of a vector from its perpendicular parts.
  • Recombine or interpret the components in the stated coordinate system and physical context.

1.4.3—A vector as two perpendicular components question 1

[Maximum number: 2]

A car travels in a straight line up a slope, as shown in Fig. 3.1.

Fig. 3.1

Fig. 3.1

The car has mass 850 kg and travels with a constant speed of 9.0 ms−19.0 \mathrm{~ms}^{-1}. The car's engine exerts a force on the car of 2.0 kN up the slope.

A resistive force FDF_{\mathrm{D}}, due to friction and air resistance, opposes the motion of the car.
The variation of FDF_{\mathrm{D}} with the speed v of the car is shown in Fig. 3.2.

Fig. 3.2

Fig. 3.2

Consider the forces that act along the slope. Use data from Fig. 3.2 to determine the component of the weight of the car that acts down the slope.

component of weight =
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