Mathematics 9709 · AS & A Level · Forces and equilibrium

Forces and equilibrium — practice question

Two people are towing a boat along a river. One walks on a path beside one bank, while the other walks on a path on the opposite bank. The first person applies a horizontal force of $60\text{ N}$ at an angle of $25^\circ$ to the river’s direction. The second person applies a horizontal force of $50\text{ N}$ at an angle of $15^\circ$ to the river’s direction (see diagram).
(i)[2]

Find the total force exerted by the two people in the direction of the river.

(ii)[4]

Find the magnitude and direction of the resultant force exerted by the two people.

Worked solution & mark scheme

This 6-mark question has a full step-by-step worked solution and mark scheme. One marking point: Resolve the forces in the river’s direction, e.g. $X = 60\cos25 + 50\cos15$

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