Question 7 - 15 marks You should be able to answer this question after studying Unit 10. A basketball player throws a basketball at an angle of 65 to the horizontal and at a speed of 5 ms . The basketball is at a height of 2m above the ground when it leaves the basketball player's hand. Set up coordinate axes at the point where the ball leaves the player's hand. Let i and j be the Cartesian unit vectors in the positive directions of the x- and y-axes respectively, as shown in the following diagram. lv| = 5ms-1 650 2 m Model the ball as a particle and assume that the only force acting on it is its 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 ball t seconds after leaving the player's hand is given by r = 5t cos 65 i + (5t sin 650 - 2gt2) j. [8] (b) The ball passes from above through a basketball hoop, which is 3m above the ground. (i) Find the time (in seconds) that it takes for the ball to reach the hoop . [5] (ii) Determine the horizontal distance (in metres) between the point at which the ball leaves the player's hand and the point where it reaches the hoop. [2]