1. 1
   A cargo ship's navigator records that the ship has travelled a distance of 40 km along a winding shipping route, and separately records that its final position is a displacement of 40 km north-east of its starting port. The ship is also acted on by two forces: the thrust from its engine pushing it forward, and the drag force from water resistance acting backward.

   (a)

   Which of these two measurements is a vector quantity?

   [1 mark]

   • ABeing 40 km north-east of the starting port, because it has both magnitude and direction
   • BHaving travelled 40 km, because it has both magnitude and direction
   • CBoth measurements are scalar quantities
   • DNeither measurement has a magnitude

   (b)

   The ship is also acted on by two forces: the thrust from its engine pushing it forward, and the drag force from water resistance acting backward. Which statement correctly describes how to find the resultant force on the ship if these two forces act along the same line?

   [1 mark]

   • AMultiply the two forces together to find the resultant
   • BAdd the two forces together, since force is always a scalar quantity
   • CSubtract the smaller force from the larger force, since the forces act in opposite directions along the same line
   • DThe resultant force is always zero whenever two forces act on an object

   (c)

   The ship's engine produces a forward thrust of 500 kN, while water resistance produces a backward drag force of 350 kN. Calculate the resultant force acting on the ship, stating its size and direction.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A skydiver jumps from a plane and begins to fall towards the ground before opening their parachute. Their mass, including equipment, is 80 kg.

   (a)

   Before opening their parachute, which two forces act on the skydiver as they fall?

   [1 mark]

   • AWeight acting upward and air resistance acting downward
   • BWeight acting downward and air resistance acting upward
   • COnly weight acts on the skydiver, since air has no effect on falling objects
   • DOnly air resistance acts on the skydiver, since weight only applies to stationary objects

   (b)

   The skydiver has a mass of 80 kg, including all equipment. Using gravitational field strength g = 9.8 N/kg, what is the skydiver's weight?

   [1 mark]

   • A7840 N
   • B80 N
   • C8.16 N
   • D784 N

   (c)

   Explain what happens to the resultant force on the skydiver, and to their velocity, as they fall for longer before reaching terminal velocity.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A tug-of-war team pulls a rope with a force of 600 N at an angle to the ground, rather than pulling it perfectly horizontally, during a competition on a sports field.

   (a)

   Using the idea of resolving a force into components, explain why only part of the 600 N force actually contributes to pulling the rope along the ground.

   [3 marks]

   (b)

   During the same tug-of-war competition, two teams pull on opposite ends of the rope, with team A applying 4200 N and team B applying 3900 N, both acting horizontally along the line of the rope in opposite directions. A free body diagram is used to show these two forces. Describe how the free body diagram would represent the two teams' forces, calculate the resultant force on the rope, and state which team the rope will move towards.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A civil engineer is designing a suspension bridge and must consider the various forces acting on different parts of the structure. The main supporting cable is pulled by the weight of the deck below it and held up by tension forces from two anchor points, each acting at a different angle.

   (a)

   Explain the difference between scalar and vector quantities, and discuss why representing forces as vectors, rather than simply as numbers, is essential when analysing a structure like a bridge.

   [6 marks]

   (b)

   The engineer models the main supporting cable of the bridge as being pulled by the weight of the deck below it and held up by tension forces from two anchor points, each acting at a different angle. Explain how the engineer could use vector diagrams and free body diagrams to determine whether the cable is in equilibrium, and discuss why this analysis matters for the safety of the finished bridge.

   [6 marks]

   Total for question 4: 12 marks

End of questions