Choose only 1 of the following problems to answer. All steps and justification must be provided for full marks. If you submit more than one problem, only the FIRST problem will be marked, and you will lose one mark for not following instructions.
You are expected to use exact values in your solution and round only your final answer, if applicable. Using estimated values (rounded decimals) will lead to marks deduction.
Remember to state the Problem number that you have chosen in your solution. (1 mark deduction in Communication for not stating it clearly.)
Problem 1 A toy rocket powered by air compression is launched vertically upward off a 5-m tall platform. The height of the rocket, h(t), in metres, can be approximated by the function h(t) = -5t² + 20t + 10, where t is the time, in seconds, after the rocket is launched. a) Sketch the graph. b) How high is the rocket after 1 s? c) What is the maximum height of the rocket? d) How long does it take the rocket to reach its maximum height? e) When will the rocket fall onto the ground?
Problem 2 Whales are known to “breach” or leap out of water. The breach of a Humpback whale can be approximated by the equation h = -4.9t² + 6.2t – 0.4, where h represents the height from the surface of the water, in metres, and t is the time since the whale reaches maximum speed, in seconds. a) What do the h- and t-intercepts represent? b) How high is the whale after 0.4 s? c) What is the maximum height a whale can breach? d) How long does the whale take to reach the maximum height? e) How long is the whale above the water surface, to the nearest hundredth of a second?
Problem 3 The cross section of a river is found to be in parabolic shape approximated by the equation g(d) = 0.008d²-0.92d, where the x-axis represents the water surface. When g(d) = -1, it means that the river has a depth of 1 metre at this point and the distance from one shore is d metres. a) How wide is this cross section? b) What is the deepest depth of this cross section? c) If a ferry reaches 2 m deep into the water, how far away from shore (the least distance) should the dock be built so that the ferry will not touch land? Assume that the sides of the ferry will not touch the riverbed.
Problem 4 A ball is thrown vertically upward off the roof of a 50-m tall building. The height of the ball, h(t), in metres, can be approximated by the function h(t) = -5t² + 12t + 50, where t is the time, in seconds, after the ball is thrown. a) What is the domain of this function? b) How high is the ball after 3 s? c) Find the maximum height of the ball. d) How long does it take the ball to reach its maximum height? e) When will the ball touch the ground?