Net Change Theorem: Solving for Time of Ball Dropped from 6 Story Building

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SUMMARY

The discussion centers on calculating the time it takes for a ball, thrown upward at 90 ft/sec from the top of a 6-story building, to land on the sidewalk below. The integral setup provided is _{0}∫^{t} 90t dt, referencing the fundamental theorem of calculus. Participants emphasize the importance of demonstrating effort in problem-solving before seeking assistance. The conversation highlights the necessity of applying calculus principles to derive the solution effectively.

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  • Understanding of basic calculus concepts, particularly integration.
  • Familiarity with the fundamental theorem of calculus.
  • Knowledge of kinematic equations for projectile motion.
  • Ability to interpret and manipulate mathematical expressions.
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  • Study the application of the fundamental theorem of calculus in real-world problems.
  • Learn about kinematic equations for vertical motion, specifically for objects under gravity.
  • Explore advanced integration techniques relevant to physics problems.
  • Practice solving similar projectile motion problems to reinforce understanding.
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Students in calculus or physics courses, educators teaching projectile motion, and anyone interested in applying calculus to real-world scenarios.

sunny12
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A ball is thrown upward at 90 ft/sec from the top of a 6 story building. How long will it take before the ball lands on the sidewalk below?

This is what I have so far:

[itex]_{0}[/itex]∫[itex]^{t}[/itex] 90t dt

General statement for the fundamental theorem of calculus ([itex]_{a}[/itex]∫[itex]^{b}[/itex] f(x) dx=F(b)-F(a)).
 
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We aren't really supposed to help you if you haven't followed a form similar to what is laid out for you when you begin a post, and especially not if you haven't shown any effort in completing the problem yourself.

Why don't you tell us what you've done so far, and where you are having trouble, and we can help you from there.
 

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