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1. The motion of a ball, whether thrown or kicked, follows a

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1. The motion of a ball, whether thrown or kicked, follows a… 1. The motion of a ball, whether thrown or kicked, follows a parabolic path. Your enthusiastic class was watching a football game one Friday afternoon. As usual, your math teacher was busy analyzing a field goal kick and noticed that the kicker was 3 meters from the uprights (goal posts). Knowing that the crossbar was 3 meters above the ground, it was estimated that the football sailed through the goal posts at a whopping 9 meters above the ground. Here’s a picture you can visualize:a) Assuming that the vertex of the path occurs when it crosses the posts (that is, it travels another 3 meters after the posts), sketch the path of the ball in the grid below. HINTS: ? Place points down for the vertex and the zeroes first. ? Then work on the step pattern. ? The x-axis represents the ground. ? The ball is kicked at (0,0).b) Write the equation of the parabola above in vertex form.?INT: You will need the vertex and the step pattern. NOTE THE DIRECTION OF OPENING!! c) Write the equation of the parabola in standard form. HINT: Expand and collect like terms. d) What are the zeroes (x intercepts) of the parabola and what do they represent in the scenario? e) How high is the ball when it is 2 meters from the kicker? f) When the ball is 5 meters high, how far is it from the kicker? g) The crossbar is 3 meters above the ground. If the kicker is 1 meter from the goal posts, will the field kick be good (that is, will it make it over the crossbar)? [1 mark] HINT: Use the graph you sketched. The goal posts were originally 3 meters from the kicker. h) If the speed of the ball was 36 m/s, how long was the football in the air?MathStatistics and ProbabilitymatlabMHF4U 101

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