Please answer the following questions:

Q1 . A plane is dropping packets of aid as it ies over a ooded village. The speed of a packet when it leaves the plane is 60 m si. The packet has mass 25 kg. The packet fails a vertical distance of 34 metres to reach the ground. (a) Calculate the kinetic energy of the packet when it leaves the plane. (2} (b) Calculate the potential energy lost by the packet as it falls to the ground. (2) (c) Assume that the effect of air resistance on the packet as it falls can be neglected. (i) Find the kinetic energy of the packet when it reaches the ground. (2) (ii) Hence nd the speed of the packet when it reaches the ground. (2) (Total B marks) Q2. When a car, of mass 1200 kg, travels at a speed of v m s-1 it experiences a total resistive force which can be modelled as being of magnitude 36v newtons. The maximum power of the car is 90 kilowatts. The car starts to descend a hill, inclined at 5.2\" to the horizontal, along a straight road. Find the maximum speed of the car down this hill. (Total 5 marks) Q3. A bungee jumper, of mass 80 kg, is attached to one end of a light elastic cord. of natural length 16 metres and modulus of elasticity 784 N. The other end of the cord is attached to a horizontal platform, which is at a height of 65 metres above the ground. The bungee jumper steps off the platform at the point where the cord is attached and falls vertically. The bungee jumper can be modelled as a particle. Hooke's law can be assumed to apply throughout the motion and air resistance can be assumed to be negligible. (a) Find the length of the cord when the acceleration of the bungee jumper is zero. (4) (b) The cord extends by x metres beyond its natural length before the bungee jumper rst comes to rest. (i) Show that):2 - 32x - 512 = 0. (4} (ii) Find the distance above the ground at which the bungee jumper rst comes to rest. (4) (Total 12 marks)