The dimensions of a badminton court are as shown below in plan view. 1.9812m ¾ - 6 X 6 j 6 6.096m 5.1816m A i - k ¼ ? ? O ¾ - 6.7056m A player at the pointO smashes the shuttlecock from a pointY at a height of 3.00m vertically aboveO. Assume that the shuttlecock then travels in a straight line directly over the net at the midpointA, which is at a height of 1.55m, before bouncing at the pointX. The unit vector k is directed vertically upwards. (a) Taking the origin atO and axes as shown in the ?gure, write down the position vectors of the pointsY andA. [2] (b) Determine the position vector of any point on the lineYA, and hence ?nd the position vector of the pointX. Deduce that the shuttlecock cannot land in the shaded area of the court. [7] (c) Find the distance travelled by the shuttlecock between the point of the smash and hitting the ?oor. [2] --? --? (d) Find the dot product of the vectorsXO andXY, and hence determine the angle below the horizontal at which the shuttlecock travels before landing. Give your answer in degrees correct to two decimal places. [4] --? --? (e) Find the cross product of the vectorsYX andYO, and use this result to determine the area of the triangleOYX and a unit vector --? --? perpendicular toYX andYO. [6] Question 6 (Unit 4) – 3 marks Consider the vector v shown in the following diagram. 6 j 6 i - v Y ? - Find the i- and j-components of v in terms of the magnitude of v and?, simplifying your answers as far as possible. [3] page 7 of 22
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