Turn over 15 Question 4 continued _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ (Total for Question 4 is 10 marks) 16 5. N 45° O 25 m A U m s−1 100 m Figure 2 A small ball is projected with speed U m s−1 from a point O at the top of a vertical cliff. The point O is 25 m vertically above the point N which is on horizontal ground. The ball is projected at an angle of 45° above the horizontal. The ball hits the ground at a point A, where AN = 100 m, as shown in Figure 2. The motion of the ball is modelled as that of a particle moving freely under gravity. Using this initial model, (a) show that U = 28 (6) (b) find the greatest height of the ball above the horizontal ground NA. (3) In a refinement to the model of the motion of the ball from O to A, the effect of air resistance is included. This refined model is used to find a new value of U. (c) How would this new value of U compare with 28, the value given in part (a)? (1) (d) State one further refinement to the model that would make the model more realistic. (1) _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________