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6. A ball is thrown straight up in the air at time t = 0. Its height y(t) is given by 1 291² y(t) = vot (1) Calculate: (a) The time at which the ball hits the ground. First, make an estimate using a scaling analysis (the inputs are g and vo and the output is the time of landing. Think about their units and how you might construct the output using the inputs, just by matching units). Solve the problem exactly. Verify that the scaling analysis gives you (almost) the correct answer. (b) The times at which the ball reaches the height v/(4g). Use the quadratic formula. (c) The times at which the ball reaches the height v/(2g). You should find that both solutions are identical. What does this indicate physically? (d) The times at which the ball reaches the height v/g. What is the physical interpretation of your solutions? (e) Does your scaling analysis provide any insight into the answers for questions (a-e)? Discuss. (Hint: Observe how your answers depend on g and vo).

6. A ball is thrown straight up in the air at time t = 0. Its height y(t) is given by 1 291² y(t) = vot (1) Calculate: (a) The time at which the ball hits the ground. First, make an estimate using a scaling analysis (the inputs are g and vo and the output is the time of landing. Think about their units and how you might construct the output using the inputs, just by matching units). Solve the problem exactly. Verify that the scaling analysis gives you (almost) the correct answer. (b) The times at which the ball reaches the height v/(4g). Use the quadratic formula. (c) The times at which the ball reaches the height v/(2g). You should find that both solutions are identical. What does this indicate physically? (d) The times at which the ball reaches the height v/g. What is the physical interpretation of your solutions? (e) Does your scaling analysis provide any insight into the answers for questions (a-e)? Discuss. (Hint: Observe how your answers depend on g and vo).

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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6. A ball is thrown straight up in the air at time t = 0. Its height y(t) is given by y(t) = vot - 791² (1) Calculate: (a) The time at which the ball hits the ground. First, make an estimate using a scaling analysis (the inputs are g and vo and the output is the time of landing. Think about their units and how you might construct the output using the inputs, just by matching units). Solve the problem exactly. Verify that the scaling analysis gives you (almost) the correct answer. (b) The times at which the ball reaches the height v/(4g). Use the quadratic formula. (c) The times at which the ball reaches the height v/(2g). You should find that both solutions are identical. What does this indicate physically? (d) The times at which the ball reaches the height v/g. What is the physical interpretation of your solutions? (e) Does your scaling analysis provide any insight into the answers for questions (a-e)? Discuss. (Hint: Observe how your answers depend on g and vo).
Transcribed Image Text:6. A ball is thrown straight up in the air at time t = 0. Its height y(t) is given by y(t) = vot - 791² (1) Calculate: (a) The time at which the ball hits the ground. First, make an estimate using a scaling analysis (the inputs are g and vo and the output is the time of landing. Think about their units and how you might construct the output using the inputs, just by matching units). Solve the problem exactly. Verify that the scaling analysis gives you (almost) the correct answer. (b) The times at which the ball reaches the height v/(4g). Use the quadratic formula. (c) The times at which the ball reaches the height v/(2g). You should find that both solutions are identical. What does this indicate physically? (d) The times at which the ball reaches the height v/g. What is the physical interpretation of your solutions? (e) Does your scaling analysis provide any insight into the answers for questions (a-e)? Discuss. (Hint: Observe how your answers depend on g and vo).
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