The dimensions of a badminton court are as shown below in plan view. O A X 6.096m 6? 5.1816m 6? ¾ 6.7056m -1.¾981-2m 6 j -i k¼ A player at the point O smashes the shuttlecock from a point Y at a...

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The dimensions of a badminton court are as shown below in plan view. O A X 6.096m 6? 5.1816m 6? ¾ 6.7056m -1.¾981-2m 6 j -i k¼ A player at the point O smashes the shuttlecock from a point Y at a height of 3.00m vertically above O. Assume that the shuttlecock then travels in a straight line directly over the net at the midpoint A, which is at a height of 1.55m, before bouncing at the point X. The unit vector k is directed vertically upwards. (a) Taking the origin at O and axes as shown in the figure, write down the position vectors of the points Y and A.


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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



Answered Same DayDec 23, 2021

Answer To: The dimensions of a badminton court are as shown below in plan view. O A X 6.096m 6? 5.1816m 6? ¾...

Robert answered on Dec 23 2021
114 Votes
The dimensions of a badminton court are as shown below in plan.
A player at the point O smashes the
shuttlecock from a point Y at a height of 3.00 m vertically above O.
Assume that the shuttlecock then travels in a straight line directly over the net at the midpoint A, which
is at a height of 1.55 m, before bouncing at the point X. The unit vector k is directed vertically upwards.
(a) Taking the origin at O and axes as shown in the figure, write down the position vectors of
the points Y and A.
Sol:
̂ ̂ ̂
Given, A is midpoint
Hence its Y – coordinate is given by,5.1816/2=2.0908
Position vector of A is given by,
̂ ̂ ̂
O
6.096 m
6.7056 m
1.9812
5
.1
8
1
6

X
A
i
j
k
(b) Determine the position vector of any point on the line Y A, and hence find the position
vector of the point X . Deduce that the shuttlecock cannot land ...
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