1. Define a model (equation) to express the vertical position (height) of the rocket s (in meters) above ground level t seconds after launch. Let g = 32 ft/sec2. 2. Graph your equation with time on the horizontal axis and height on the vertical axis. Let the values for time range from 0 to 10 seconds and the values for the height range from 0 to 200 feet. Include your graph in this response. 3. Refer to your graph in Question 2. Explain what the vertex, x-intercept, and y-intercept represent in the context of this problem. 4. Calculate the time(s) at which the rocket is at a height of 40 ft. (Round to 1 decimal place.) Is this the maximum height the rocket will reach? Justify your response. 5. Calculate the time(s) at which the rocket is at a height of at least 85 ft above the ground. Round to the nearest hundredth. Explain your answer.
Scenario: A toy rocket is launched straight upward from a pad 10 ft above ground level with an initial velocity of 80 ft/sec.
Use the general formula for the vertical position (height) of an object moving under the influence of gravity ?= ―1/ 2??^2 + ?0?+ ?0 where s0 is initial vertical position, v0 is initial
velocity, and s is vertical position of the object.
1. Define a model (equation) to express the vertical position (height) of the rocket s (in meters) above ground level t seconds after launch. Let g = 32 ft/sec2.
2. Graph your equation with time on the horizontal axis and height on the vertical axis. Let the values for time range from 0 to 10 seconds and the values for the height range from 0 to 200 feet. Include your graph in this response.
3. Refer to your graph in Question 2. Explain what the vertex, x-intercept, and y-intercept represent in the context of this problem.
4. Calculate the time(s) at which the rocket is at a height of 40 ft. (Round to 1 decimal place.) Is this the maximum height the rocket will reach? Justify your response.
5. Calculate the time(s) at which the rocket is at a height of at least 85 ft above the ground. Round to the nearest hundredth. Explain your answer.
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