The height s at time t of a silver dollar dropped from the World Trade

In summary, the equation for finding the height of the silver dollar at a given time t is s(t) = -16t^2 + h, where h is the initial height from which the silver dollar was dropped. The time it takes for the silver dollar to reach the ground can be found by setting s(t) = 0 and solving for t. This will give you the time it takes for the silver dollar to reach the ground, also known as the time of impact. Yes, the initial height of the silver dollar can be negative. This would indicate that the silver dollar was dropped from a height below ground level. The acceleration of the silver dollar as it falls is -32 feet per second squared. This is because of the
  • #1
Yyyanngg
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Homework Statement
The height s at time t of a silver dollar dropped from the World Trade center is given by
s=−16t2+1350
where s is measured in feet and t is measured in seconds.
a) Find the average velocity on the interval [1, 2].
b) Find the instantaneous velocity when t=1 and t=2.
Relevant Equations
The height s at time t of a silver dollar dropped from the World Trade center is given by
s=−16t2+1350
where s is measured in feet and t is measured in seconds.
I don't have any solution
 
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  • #2
Can you write down a function to give the instantaneous velocity?
 
  • #3
This is standard stuff found elementary textbooks, or that you can find by googling "Motion under uniform acceleration", that tie together distance travelled, velocity, acceleration and time.

If there is anything special about this, this is the unusual nonmetric units that you will have to be careful about.
 

1. What is the formula for calculating the height of the silver dollar at a given time?

The formula for calculating the height (s) of the silver dollar at a given time (t) is s = -16t^2 + h, where h is the initial height of the silver dollar when it was dropped from the World Trade Center.

2. How long does it take for the silver dollar to hit the ground?

Using the same formula as above, we can solve for t when s = 0. This will give us the time it takes for the silver dollar to hit the ground. Keep in mind that this assumes no air resistance and a constant acceleration due to gravity.

3. What is the initial height of the silver dollar when it was dropped from the World Trade Center?

The initial height (h) of the silver dollar can be determined through observation or measurement. It is the height at which the silver dollar was dropped from the World Trade Center.

4. How does air resistance affect the height of the silver dollar?

Air resistance can affect the height of the silver dollar by slowing down its descent. This means that the actual height of the silver dollar at a given time will be slightly higher than what is calculated using the formula mentioned above. However, for objects dropped from a relatively low height like the World Trade Center, the effect of air resistance is minimal.

5. Can this formula be used for objects dropped from any height?

Yes, this formula can be used for objects dropped from any height as long as the initial height is known. Keep in mind that this formula assumes no air resistance and a constant acceleration due to gravity, so it may not be accurate for objects dropped from extreme heights or in environments with varying air resistance.

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