Imagine a scenario involving a bungee jumper leaping from a bridge, with the jumper's height above the river surface modeled by the equation h(t) = -0.5t2 + v0t + h0 , where h is measured in meters, t is in seconds, v0 represents the jumper's initial velocity in meters per second, and h0 is the initial height above the river. Given v0 = 0 m/sec and h0 = 210 meters. (i) Based on this scenario, answer the following questions that are related to the mathematical understanding of the concept: (a) What is the domain and range of h(t)? What is the physical significance of domain and range in this scenario? (b) What is the vertex of the given height function, h(t) = -0.5t2 + v0t + h0? What does the vertex represent in this scenario? (c) At what time does the bungee jumper reach maximum height and what is the maximum height? Explain using the formula and scenario. (d) At what time does the bungee jumper reach the height of 11m? (e) What is the height after 20 seconds of the jump, and what does this situation represent? (f) When will the bungee jumper touch the river? (ii) Based on that scenario, answer the following questions that related to the graphical understanding of the concept: (a) Draw the graph of the given height function, h(t) = -0.5t2 + v0t + h0 (b) By observing the graph, determine the time intervals in which the height is increasing or decreasing. (c) Find the axis of symmetry on the graph and explain the above scenario using the axis of symmetry. (d) What are the t and h intercepts on the axes here? What do they represent in this scenario?
Imagine a scenario involving a bungee jumper leaping from a bridge, with the jumper's height above the river surface modeled by the equation h(t) = -0.5t2 + v0t + h0 , where h is measured in meters, t is in seconds, v0 represents the jumper's initial velocity in meters per second, and h0 is the initial height above the river. Given v0 = 0 m/sec and h0 = 210 meters.
(i) Based on this scenario, answer the following questions that are related to the mathematical understanding of the concept:
(a) What is the domain and range of h(t)? What is the physical significance of domain and range in this scenario?
(b) What is the vertex of the given height function, h(t) = -0.5t2 + v0t + h0? What does the vertex represent in this scenario?
(c) At what time does the bungee jumper reach maximum height and what is the maximum height? Explain using the formula and scenario.
(d) At what time does the bungee jumper reach the height of 11m?
(e) What is the height after 20 seconds of the jump, and what does this situation represent?
(f) When will the bungee jumper touch the river?
(ii) Based on that scenario, answer the following questions that related to the graphical understanding of the concept:
(a) Draw the graph of the given height function, h(t) = -0.5t2 + v0t + h0
(b) By observing the graph, determine the time intervals in which the height is increasing or decreasing.
(c) Find the axis of symmetry on the graph and explain the above scenario using the axis of symmetry.
(d) What are the t and h intercepts on the axes here? What do they represent in this scenario?
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