A projectile problem (Olympiad)

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Homework Help Overview

The problem involves a rock launched vertically, with the condition that during the last second of its flight, it covers half of the total distance traveled. Participants are exploring the implications of this scenario in the context of projectile motion.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants discuss the implications of ignoring air resistance and question the assumption that the rock must return to the ground. They explore the idea of the rock potentially continuing its ascent or descending without landing.

Discussion Status

The discussion is ongoing, with participants sharing their thoughts on the problem setup and exploring various interpretations. Some guidance has been offered regarding simplifying assumptions, but no consensus has been reached on the correct approach or solution.

Contextual Notes

Participants note that the problem does not explicitly state whether the rock returns to the ground, leading to different interpretations of the flight duration. There is also mention of complications arising from considering air resistance.

Michael Si
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A rock is launched vertically. During the last second of the flight, the rock covers one-half of the entire distance covered during the flight. What is the maximum possible duration of the flight? (Hint: answer is not 2 seconds.)

I've tried to use integration to solve an equation of motion which includes air resistance but failed. Anyone can help me?
 
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Welcome to PF!

Michael Si said:
A rock is launched vertically. During the last second of the flight, the rock covers one-half of the entire distance covered during the flight. What is the maximum possible duration of the flight? (Hint: answer is not 2 seconds.)

I've tried to use integration to solve an equation of motion which includes air resistance but failed. Anyone can help me?

Hi Michael! Welcome to PF! :smile:

i] ignore air resistance (this is a standard uniform-acceleration problem)

ii] you have noticed the question doesn't say the rock returns? :wink:

ii] show us what you've tried, and where you're stuck, and then we'll know how to help. :smile:
 
Thank you. :smile: Well, you're right. Since the conditions aren't clearly stated, factors like air-resistance can be ignored so as to simplify the problem. And indeed, the rock would not necessarily return. But I am not sure where the rock would be if i doesn't fall back. :rolleyes:

If it follows a simple projectile trajectory (in which it falls back to the ground) without resistance and assuming constant acceleration, the answer would be 2 seconds, which isn't the desired answer. Then I considered air drag and formed and solved the differential equation m*dv/dt=mg-Dv^2, which gave me very complicated results. I knew it wasn't the right way then.

If the rock doesn't fall back, where would it go?
 
Michael Si said:
If the rock doesn't fall back, where would it go?

Well … either up or down!

"flight" doesn't include landing … :smile:
 

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