Relative to a point O, the position vector of a ship is (12 i+16 j)km. If the ship sails with a constant speed of 24km//h on a bearing of 060^(@), find its position vector after 4 hours. Give your answer correct to 3 significant figures.

Question

Relative to a point  O, the position vector of a ship is  (12 i+16 j)km. If the ship sails with a constant speed of  24km//h on a bearing of  060^(@), find its position vector after 4 hours. Give your answer correct to 3 significant figures.

Bytelearn · Accepted Answer

Calculate displacement vector:  Calculate the displacement vector after 4 hours. The ship travels at 24 km/h and sails for 4 hours. Distance = speed × time = 24 km/h × 4 h = 96 km.Convert bearing to direction angle:  Convert the bearing to a direction angle. A bearing of 060° corresponds to 60° north of east. This is 30° from the positive x-axis (east direction).Calculate components using trigonometry:  Calculate the components of the displacement vector using trigonometry. Using the direction angle: x-component = 96 km × cos(30°) = 96 × 0.866 = 83.136 km, y-component = 96 km × sin(30°) = 96 × 0.5 = 48 km.Add initial position vector:  Add the initial position vector to the displacement vector. Initial position vector = (12i + 16j) km, Displacement vector = (83.136i + 48j) km, New position vector = (12 + 83.136)i + (16 + 48)j = (95.136i + 64j) km.

Relative to a point $O$ , the position vector of a ship is $(12 i+16 j) \mathrm{km}$ . If the ship sails with a constant speed of $24 \mathrm{~km} / \mathrm{h}$ on a bearing of $060^{\circ}$ , find its position vector after $4$ hours. Give your answer correct to $3$ significant figures.

Full solution

More problems from Find the magnitude and direction of a vector sum

Related topics