3. Take 3 = ll] ms" in this question. Air resistance should be neglected. A ball is thrown from a point 0 with a velocity of 15 rns'l at an angle off? to the horizontal. where cos 6' = 0.6 and sin 6' = 0.8 . The diagram below shows : and _v-axes drawn through 0, the point ofprojection. The units of the axes are metres. O x (a) Show that, after ti me 1' seconds, the position of the ball is given by _=9;' y=12i5i3. [3] (b) Show that the equation of the ball is yzgxflxz. [3] {c} Hence calculate how far from the origin the hall lands. [3] 4. A stone is projected over horizontal ground from a point 0 on the groLInd. The velocity of projection is 30 ms'l at 40" to the horizontal. The effects of air resistance should be neglected. {a} State the modelling assumptions used in the standard projectile model. [2] (b) The stone is at a horizontal distance x m from the point ofprojection and _v m above the ground 1 seconds after projection. Write doWn an expressions for x and _v in terms of r. [2] The stone passes directly over a wall which is at a horizontal distance of34 m from 0. {c} Find the time taken to reach the wall. [2] Mathematics 1 m2 12.111113 E9ME| Educatn inuwbnauumg nnovu on MEI A level Maths Projectiles Assessment (d) Determine the speed ofthe stone as it passes over the wall. Calculate also the angle between the direction of motion of the ball and the horizontal at that time, making it clear whether the ball is rising or fall ing. [8]