At time t = 0, a football player kicks a ball from the point a with position vector (2i + j) m on a horizontal football field. the motion of the ball is modelled as that of a particle moving horizontally with constant velocity (5i + 8j) m s–1.
find

(a) the speed of the ball,
(b) the position vector of the ball after t seconds.

the point b on the field has position vector (10i + 7j) m.
(c) find the time when the ball is due north of b.

at time t = 0, another player starts running due north from b and moves with constant speed v m s–1. given that he intercepts the ball,

(d) find the value of v.

(e) state one physical factor, other than air resistance, which would be needed in a refinement of the model of the ball’s motion to make the model more realistic.