A rectangular football field has its corners labelled ,
MATHEMATICS · Multi-part · AP · AP Precalculus · Functions with Parameters, Vectors, and Matrices · Functions with Parameters, Vectors, and Matrices
Problem
A rectangular football field has its corners labelled A(0,0), B(100,0), C(100,70) and D(0,70) in metres with respect to a ground-fixed frame XY whose origin is corner A; the X-axis runs east and the Y-axis runs north.
(i) A ball is at position P(30,20) in the ground frame. A second frame X′Y′ is introduced with its origin O′ at the centre of the field (50,35). The X′-axis is parallel to X, but the Y′-axis points south (opposite to Y). Determine the coordinates (x′,y′) of the ball in the new frame.
(ii) The ball is kicked to point Q(80,10) in the ground frame. Calculate the displacement vector of the ball for the kick in both frames and verify that the magnitude of the displacement is the same in each frame.
(iii) Find the angle that the displacement makes with the positive X′-axis in the X′Y′ frame.