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

In summary, the conversation is about finding the amount of time it takes for a ball thrown upward at a velocity of 90 ft/sec from the top of a 6 story building to land on the sidewalk below. The equation _{0}∫^{t} 90t dt is mentioned, which could be related to the fundamental theorem of calculus (_{a}∫^{b} f(x) dx=F(b)-F(a)). However, the person asking for help has not provided enough information or effort in solving the problem.
  • #1
sunny12
1
0
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)).
 
Last edited:
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  • #2
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.
 

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

What is the Net Change Theorem?

The Net Change Theorem is a mathematical concept that relates the change in a quantity to the rate at which it changes. It is commonly used in physics and engineering to solve problems involving motion and changing quantities.

How is the Net Change Theorem used to solve for the time of a ball dropped from a 6-story building?

To solve for the time of a ball dropped from a 6-story building using the Net Change Theorem, we need to know the initial height of the ball, the acceleration due to gravity, and the final height of the ball when it hits the ground. We can then use the formula t = √(2Δh/g) to calculate the time, where t is the time, Δh is the change in height, and g is the acceleration due to gravity (9.8 m/s²).

What are the key steps to solving for the time using the Net Change Theorem?

The key steps to solving for the time using the Net Change Theorem are:

  • Identify the initial and final heights of the object
  • Determine the change in height (Δh)
  • Find the acceleration due to gravity (g)
  • Plug in the values into the formula t = √(2Δh/g)
  • Solve for the time (t)

Can the Net Change Theorem be used for objects dropped from any height?

Yes, the Net Change Theorem can be used for objects dropped from any height. The formula t = √(2Δh/g) takes into account the change in height and the acceleration due to gravity, regardless of the initial height of the object.

What other applications can the Net Change Theorem be used for?

The Net Change Theorem can be used in various applications, such as calculating the time it takes for a rocket to reach its destination, determining the speed of a falling object, and analyzing the rate of change in a chemical reaction. It is a versatile tool that can be applied to many real-world problems involving change and motion.

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