The diagram shows a river with parallel banks. The river is 75 m wide and is flowing with a speed of 2.4 ms⁻¹. A speedboat travels in a straight line from a point A on one bank to a point B on the opposite bank, 30 m downstream from A. The speedboat can travel at a speed of 4.5 ms⁻¹ in still water. [Figure 7.1]

Mark scheme

Marking points from the official mark scheme (May/June 2016). The mark or mark type is shown in brackets.

1. [1] Finding an angle of 68.2° or 21.8°
2. [1] 4.5/sin68.2 = 2.4/sinα
3. [1] leading to α = 29.7° (allow ±0.1)
4. [1] Direction is 82.1° to the bank, upstream (allow ±0.1°)
5. [1] 4.5/sin68.2 = Vr/sin(180 - 68.2 - 29.7)
6. [1] leading to vr = 4.8
7. [1] time taken = 80.78 / 4.8
8. [1] time taken = 16.8
9. [1] 4.5² = 2.4² + v_r² - (2 * 2.4 * v_r * cos 68.2) (Alternative method)
10. [1] leading to v_r = 4.8 (Alternative method)
11. [1] time taken = 80.78 / 4.8 (Alternative method)
12. [1] time taken = 16.8 (Alternative method)