Scalars, vectors and resolvingEdexcel A-Level Physics: Subtopic test

1. 1
   A hiker walks 6.0 km due east and then 8.0 km due north, taking 3.0 hours in total.

   (a)

   Which quantity associated with the hiker's journey is a vector?

   [1 mark]

   • AThe total distance walked
   • BThe time taken
   • CThe displacement from the start to the finish
   • DThe average speed

   (b)

   What is the magnitude of the hiker's displacement from the start?

   [1 mark]

   • A14 km
   • B10 km
   • C2.0 km
   • D48 km

   (c)

   Determine the bearing of the hiker's final position from the starting point.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A child pulls a sledge across level snow using a rope. The tension in the rope is 60 N and the rope makes an angle of 35° above the horizontal.

   (a)

   What is the horizontal component of the tension in the rope?

   [1 mark]

   • A34 N
   • B60 N
   • C73 N
   • D49 N

   (b)

   The child lifts the rope so that it is at 60° above the horizontal, with the same tension. What is now the horizontal component of the tension?

   [1 mark]

   • A30 N
   • B52 N
   • C60 N
   • D49 N

   (c)

   Calculate the vertical component of the tension in the original situation and state its direction.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A boat crosses a river 120 m wide. Its engine gives it a velocity of 3.0 m s⁻¹ relative to the water, directed at right angles to the banks. The water flows at 1.5 m s⁻¹ parallel to the banks.

   (a)

   Calculate the magnitude and direction of the boat's resultant velocity relative to the river bank.

   [3 marks]

   (b)

   Calculate how long the boat takes to cross the river and how far downstream it has drifted when it reaches the far bank.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A boat is towed by two ropes attached to the same point at its bow. Rope A pulls with a force of 300 N due north. Rope B pulls with a force of 400 N, at 60° to rope A, on the eastern side.

   (a)

   Describe how a scale diagram can be used to find the resultant of the two forces, and state the values you would expect to obtain.

   [6 marks]

   (b)

   Calculate the resultant force on the boat by resolving, and evaluate this method against the scale diagram for finding the resultant.

   [6 marks]

   Total for question 4: 12 marks

End of questions