Scalars & Vectors (CIE A Level Physics)

The speed of an aeroplane in still air is 200 km h^-1. The wind blows from the west at a speed of 85.0 km h^-1.

In which direction must the pilot steer the aeroplane in order to fly due north?

Vectors P and Q are drawn to scale.

Which diagram represents the vector (P – Q)?

A vector has magnitude R and perpendicular components P and Q, as shown in the diagram.

Which row correctly describes the perpendicular components?

A resultant force of 20 N is 30° to the horizontal.

What is the horizontal and vertical component of the resultant force?

Fig 1.1 shows three coplanar forces which are in equilibrium.

What is the value of force F?

A ship’s speed in still water is 20 km h⁻¹. A current coming from the east pushes the ship at a constant speed of 5 km h⁻¹. At what bearing should the captain direct the ship so that it travels perfectly due north?

Two forces, each of 10 N, act at a point P as shown in the diagram. The angle between the force vectors is 120° 

What is the magnitude of the resultant force?

The diagrams represent systems of coplanar forces acting at a point. The lengths of the force vectors represent the magnitudes of the forces.

Which system of forces is in equilibrium?

A glider is descending at a constant speed at an angle of 15° to the horizontal. The diagram shows the directions of the lift L, air resistance R and weight W acting on the glider.

Which vector triangle could represent the forces acting on the glider?

Figure 1.1 shows two coplanar forces, R and N, which act at point P. The angle between the forces is , where  .

What is the magnitude of the resultant force F equal to?

A boat is being pulled along by two equal forces of 700 kN, both at angle θ to the direction of motion. The boat experiences a resistive force of 40 kN. The net force on the boat is 1270 kN.

What is the value of ?