A river, which is 80m wide, flows at 2ms⁻¹ between parallel, straight banks. A man wants to row his boat straight across the river and land on the other bank directly opposite his starting point. He is able to row his boat in still water at 3 ms⁻¹. Find

Mark scheme

Marking points from the official mark scheme (May/June 2015). The mark or mark type is shown in brackets.

1. [M1] cos(x) = 2/3 oe soi
2. [A1] 48.189...° or 131.810...° or 0.8410... rad or 2.3(00...) rad oe isw with reference axis indicated by comment, e.g. “to the bank” or “upstream", etc. or clearly marked on a diagram
3. Alternatively for (i):
4. [M1] sin(y) = 2/3 oe soi
5. [A1] 41.810...° or 0.7297... or 0.73(0) rad oe isw with reference axis indicated by comment, e.g. "to the perpendicular with the bank", etc. or clearly marked on a diagram
6. If M0 then SC1 for an unsupported answer of 138.189...° or 2.4118... rad or 318.189...° or 5.5534... rad with reference axis indicated by comment, e.g. "on a bearing of" or "from North" or clearly marked on a diagram
7. [B1] Speed = √(3² - 2²) (= √5) or 3 sin 48.2 or 2 tan 48.2 or 3 cos 41.8 or 2 / tan 41.8 or √(2²+3²-2×2×3cos48.2) oe or 2.236(0...) rot to 4 or more figs or 2.24 [m/s] soi
8. [M1] time = 80 / their √5 oe or time = their 107.33... / 3
9. [A1] 35.66 to 35.8 (seconds) oe ignore subsequent rounding or attempted conversion to, e.g. minutes but A0 if answer spoiled by continuation of method if no working, so B0 M0, then allow B3 for an answer 35.66 to 35.8 oe