page 05 MARKS 8. A boat is initially at position 5 2    metres. It is moving with a constant velocity of 1 4 ms 1     . A whale is resting at the surface of the water at position 60 40       metres. (a) Determine the closest distance that the boat gets to the whale. (b) State one assumption that you have made. 9. (a) Find f (t) if  2 4 17 2 17 8 t f t t t      and  ln 0 4 f  , where 0 t . (b) If  f t  represents the velocity of a particle in m s−1, where t is the time in seconds, calculate its displacement after 3 seconds. 10. A particle C is fired vertically upwards, from horizontal ground, with speed 10.5 m s−1. At the same instant another particle D is fired vertically upwards, from a point 2 metres above the ground. (a) Find the initial speed of D given that both particles reach the same maximum height. (b) Show that, at the instant when C and D are at the same height, the particles have the same speed and are moving in opposite directions. 11. A force . . 0 3 0 5   F i j moves a body between two points on the x y plane with coordinates (16, 4) and (12, 20). The force is given in newtons, and distances are given in metres. (a) Calculate the work done by the force F. (b) Hence find the component of the force in the direction of the displacement. [Turn over 5 1 2 1 3 4 2 2