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7. A baseball player hits a ball out of the park. The equation h(t) = -2(x - 3)2 + 19 models the path of the ball, where h(t) represents the height of the ball above the ground in metres, and t represents the time in seconds. (12 marks) a) Construct a table of values to show the height of the baseball for each second it is in the air (0 to 7 seconds). (2 marks) Time (seconds) = Height of the baseball (metres) = h(t) 2(0 - 3)2 + 19 =1 -2(1 -3)2 + 19 = 11 NOUAW -2(2 - 3)2 + 19 = 17 3)~ + 19 = 19 2(4- 3)2 + 19 5-3)2 + 19 = 11 -2(6 -3)2 +19 =1 -2(7 -3)2 + 19= -13 b) Calculate the average rate of change in height for each second. What does this represent? (2 marks) Rate of change from (0,1) to (1, 11) 11 -1 10=10m/s 1 - 0 Rate of change from (1,11) to (2,17) 1= " = 6m/sRate of change from (2, 17) to (3, 19) 19 - 17 2. -2 = =2m/s Rate of change from (3, 19) to (4, 17) 17 - 19 4- 3 -2m/s Rate of change from (4,17) to (5, 11) 11 -17 20=-6m/s Rate of change from (5, 11) to (6,1) 1-11 -10 6 - 5 0 = -10m/s Rate of change from (6,1) to (7, -13) -13 - 1 7 -6 -14 m/s This represents the high speed the ball is travelling when it is initially hit. Then the ball slows down as it reaches a maximum height, before gravity begins to pull it back down at a high rate. Why does the velocity change from positive to negative? (2 marks) The velocity changes from positive to negative because the ball's initial motion is upwards (positive), but once reaching the maximum height, the ball begins falling downwards (negative). When is the velocity 0 m/s, and what does this represent? (2 marks) The velocity is Om/s at 3 seconds. This represents that the ball has reached the max height, has stopped moving, and begins heading towards the ground What is the instantaneous speed of the ball when it hits the ground? Round all answers to two decimal places. (4 marks)