A skateboarder takes off from a ramp at a speed of 12ms!, at an angle of 35 to the horizontal. The edge of the ramp is 2m above the ground. Set up coordinate axes at the point where the skateboarder leaves the edge of the ramp. Let i and j be the Cartesian unit vectors in the positive directions of the z- and y-axes respectively, as shown in the diagram below. Model the skateboarder as a particle and assume that the only force acting on them is their weight. Take the magnitude of the acceleration due to gravity to be g = 9.8ms 2. Give numerical answers to two significant figures. (a) Show that the position r (in metres) of the skateboarder seconds after leaving the edge of the ramp is given by r = 12cos35i + (12sin35 1gt)j. 8] (b) Find the time (in seconds) that it takes for the skateboarder to reach the ground. [5] (c) Determine the horizontal distance (in metres) between the point at which the skateboarder leaves the edge of the ramp and the point where they reach the ground. [2]