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Nov 2016 p42 q3
3684
A boat is being pulled along a river by two people. One of the people walks along a path on one side of the river and the other person walks along a path on the opposite side of the river. The first person exerts a horizontal force of 60 N at an angle of 25° to the direction of the river. The second person exerts a horizontal force of 50 N at an angle of 15° to the direction of the river (see diagram).
(i) Find the total force exerted by the two people in the direction of the river.
(ii) Find the magnitude and direction of the resultant force exerted by the two people.
Solution
(i) To find the total force in the direction of the river, resolve each force into its horizontal component:
\(X = 60 \cos 25^{\circ} + 50 \cos 15^{\circ}\)
Calculating gives:
\(X = 54.49 + 48.30 = 102.79 \text{ N}\)
Rounded to 103 N.
(ii) To find the magnitude and direction of the resultant force, resolve each force into its vertical component:
\(Y = 60 \sin 25^{\circ} - 50 \sin 15^{\circ}\)
Calculating gives:
\(Y = 25.35 - 12.94 = 12.41 \text{ N}\)
Now, use Pythagoras' theorem to find the magnitude: