o A particle of mass ti kg moves with constant acceleration [Ltii 0.3j} to 5'2. a Find the magnitude of the net force acting on the particle. When 1: = {I the particle has velocity [Ei + 2.5j) :11 51- h Find the speed and the direction of motion of the particle 5 seconds later. A particle moves in the plane so that its position 1rector at time tseconds is {(3.2 i + [4. + .2t3]j) :11. Find the speed of the particle when t = 2.5. o A particle of mass 113 kg starts from rest and moves under the action of a constant force [El 23m. Find how long it takes to reach the speed of 121113 1. A helicopter is initially hovering above the helipad. It sets off with constant acceleration (0.3i + 1.2j)ms-2, where the unit vectors i and j are directed east and north, respectively. The helicopter is modelled as a particle moving in two dimensions. a Find the bearing on which the helicopter is travelling. b Find the time at which the helicopter is 300 m from its initial position. c Explain in everyday language the meaning of the modelling assumption that the helicopter moves in two dimensions. 10 In this question, vectors i and j point due east and north, respectively. A port is located at the origin. One ship starts from the port and moves with velocity V1 = (31 + 4j) km h-1. a Write down the position vector at time t hours. At the same time, a second ship starts 18 km north of the port and moves with velocity V2 = (3i - 5j) kmh-1. b Write down the position vector of the second ship at time t hours. c Show that, after half an hour, the distance between the two ships is 13.5 km.d Show that the ships meet. and find the time when this happens. c How lung after the meeting are the ships 18 km apart