Page 81 - Math SL HB Sem 2

(c) The airplanes meet at point
Q.

(i) At what time do the airplanes meet?

(ii) Find the position of Q.
(6)

(d) Find the angle dbetween the paths ofthe two airplanes.
(6)
(Total l7 mark)

"l In tlris question the vecror o,n *o**",s a displacemenr due east, and the **". u",
[j) (f)
represenfs a displacement due north.

The point (0, 0) is the position of Shipple Airport The position vector 11 ofan aircraft Air One
is given by

(
/to) rz\
,, =
112.J*,[_ sl,

where t is the time in minutes since l2:00.

(a) Show that rhe lir One airc,:aft

(i) is 20 km frorn Sftpp le Airport at t2:00;

(iD has a speed of l3 km/min.
(4)

(b) Show that a cartesian equation ofthe path of Air One is:
5x + l2v:224.
(3)

The position vector 12 of an aircraft Air Two is given by

,,= (")*,(").
\-51 (. 6,/

where , is the time in minutes since l2:00.

(c) Find the angle between the paths ofthe two aircraft.
(4)
(d) (i) Find a carlesian equation for the path of Air Two.

(ii) Hence find the coordinates ofthe point where the two paths cross.
(s)

(e) Given that the two aircraft are flying at the same height, show that they do not collide.
(4)
(fotal 20 marks)
l8 Questionbank Maths SL 3