2. Suppose you throw an object from a great height, so that it reaches very nearly terminal velocity by time it hits the ground. By measuring the impact, you determine that this terminal velocity is -49 mlsec. A. Write the equation representing the velocity v(e) of the object at time i seconds given the initial velocity vo and the fact that acceleration due to gravity is-98 misec². (Here, assume you're modeling the falling body with the differential equation = 8- kv, and use the resulting formula for v(e) found in the Tutorial. Of course, you can derive it if you'd like.) B. Determine the value of k, the "continuous percentage growth rate" from the velocity equation, by utilizing the information given concerning the terminal velocity. C. Using the value of k you derived above, at what velocity must the object be thrown upward if you want it to reach its peak height after 3 sec? Approximate your solution to three decimal places, and justify your answer.
2. Suppose you throw an object from a great height, so that it reaches very nearly terminal velocity by time it hits the ground. By measuring the impact, you determine that this terminal velocity is -49 mlsec. A. Write the equation representing the velocity v(e) of the object at time i seconds given the initial velocity vo and the fact that acceleration due to gravity is-98 misec². (Here, assume you're modeling the falling body with the differential equation = 8- kv, and use the resulting formula for v(e) found in the Tutorial. Of course, you can derive it if you'd like.) B. Determine the value of k, the "continuous percentage growth rate" from the velocity equation, by utilizing the information given concerning the terminal velocity. C. Using the value of k you derived above, at what velocity must the object be thrown upward if you want it to reach its peak height after 3 sec? Approximate your solution to three decimal places, and justify your answer.
Related questions
Question
Transcribed Image Text:2. Suppose you throw an object from a great height, so that it reaches very nearly terminal
velocity by time it hits the ground. By measuring the impact, you determine that this terminal
velocity is -49 m/sec.
A. Write the equation representing the velocity v() of the object at time i seconds given the
initial velocity vo and the fact that acceleration due to gravity is -9.8 m/sec2. (Here, assume
you're modeling the falling body with the differential equation d = g- kv, and use the resulting
formula for v(0) found in the Tutorial. Of course, you can derive it if you'd like.)
B. Determine the value of k, the "continuous percentage growth rate" from the velocity
equation, by utilizing the information given concerning the terminal velocity.
C. Using the value of k you derived above, at what velocity must the object be thrown upward if
you want it to reach its peak height after 3 sec? Approximate your solution to three decimal
places, and justify your answer.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps
