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Thinking: /40 Name: __________________________________________ MCF3M FUNCTIONS AND APPLICATIONS WORD PROBLEMS ASSIGNMENT Question One The quadratic relation h(t ) 0.05t 2 20 describes the path of a rock that falls from the top of a cliff, with h representing the height in metres and t representing the time in seconds. a. What is the height of the cliff? b. How long will it take the rock to reach the bottom of the cliff? c. How far from the bottom of the cliff is the rock when half of the time has passed? Question Two A penny is dropped into a tank of water at the water’s surface. If falls to the bottom according to the relation d (t ) 7.5t 2 75t , where d is the depth of the water measured in metres and t is the time after the penny was dropped, measured in seconds. a. How deep is the tank of water? b. How long will it take for the penny to reach the bottom of the tank? Question Three A rocket firework follows a parabolic path. Its height, h, in metres is given by h(t ) 5t 2 30t 12 . t is the time in seconds since it was fired. a. At what height was the firework fired? b. How many seconds was the rocket in the air? c. What is the maximum height reached by the rocket? Question Four A diver jumps from a 10-m platform. Her height, h, in metres above the water, after t seconds, can be approximated by the function h(t) = 5t 2 + 5t + 10. a. b. c. d. Determine the maximum height of the diver above the water The time at which she reaches the maximum height. How high above the water is the diver after 3 s? At what time does the diver hit the water? Question Five A ball is thrown vertically upward off the roof of a 34 m tall building. The height of the ball h(t), in metres, can be approximated by the function h(t) = -5t2 + 10t + 34, where t is the time, in seconds, after the ball is thrown. Find the maximum height of the ball. Question Six A Frisbee is passed to another teammate in a game of Ultimate Frisbee. The Frisbee follows the path h(d ) 0.02d 2 0.4d 1, where h(d) is the height, in metres, and d is the horizontal distance, in metres, that the Frisbee travelled from the thrower. a. What is the maximum height of the Frisbee? b. What is the horizontal distance from the thrower at the maximum height? c. How high was the Frisbee when it was first thrown? Question Seven The path of a soccer ball kicked from the ground is given by h(d ) 0.035d 2 d , where h(d0 is the height of the ball, in metres, and d is the horizontal distance travelled by the ball in metres. How far away did the ball land, to the nearest tenth of a metre? Question Eight When Michael drives his dirt bike off a ramp, his flight path can be modelled by h(d ) 0.57d 2 3.7d 2.5 , where d is the horizontal distance from the ramp in metres, and h(d) is his height in metres. How far away from the end of the ramp did he land, to the nearest metre? Question Nine The table shows the curve of a parabolic arch at the entrance to a park where x is the horizontal distance from one side of the arch, and h is the height of the arch above the ground, both in metres. a. Determine the quadratic model in Vertex Form. b. Determine the quadratic model in Standard Form. x 0 10 20 30 40 h(x) 0 7.5 10 7.5 0 Question Ten The table shows the path of a ball kicked into the air over time a. Determine the quadratic model in Vertex Form. b. Determine the quadratic model in Standard Form. t 0 10 20 30 40 h(t) 0 300 400 300 0