Vectors in Two Dimensions Structured Questions | Cambridge IGCSE Additional Mathematics

Additional Mathematics 0606 · Question 1Paper 2 · Calculator[10 marks]

A motorboat travels across a wide river in which the current flows from West to East at a constant speed of $2.5\text{ m s}^{-1}$ . The motorboat has a speed of $6.5\text{ m s}^{-1}$ in still water. Let unit vectors $\mathbf{i}$ and $\mathbf{j}$ point due East and due North respectively.

(a)

If the motorboat is steered due North across the river, write down its resultant velocity vector and calculate its speed over the riverbed to 3 significant figures.

[3]

(b)

Determine the bearing (to 1 decimal place) on which the motorboat must be steered so that its resultant velocity is due North.

[4]

(c)

Calculate the resultant speed of the motorboat when it is steered on the bearing found in part (b).

[3]