average, instanteous rate of change in height of flowerpot falling to the ground

Armanmbm

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Hey i had this problem on my test today and couldnt figure out anyway to solve it since i dont have the base function



4. A student is cleaning the outside of the patio windows at his aunt's apartment, which is located 90 meters above the ground. He accidentally kicks a flowerpot, sending it over the edge of the balcony.

a) Determine an algebraic expression, in terms of a and h, to represent the average rate of change of the height above the ground of the falling flowerpot. Simplify your expression.

b) Determine the average rate of change of the flowerpot's height above the ground in the interval between 1 second and 3 seconds after it fell from the edge of the balcony.

c) Estimate the instantaneous rate of change of the flowerpot's height in 1 second and at 3 seconds.

d) Determine the equation of the tangent at t = 1. Sketch a graph of the curve and tangent at t = 1.




i noticed AFTER the test that i could use the gravity number 9.8 m/s im still not sure how to solve it
 

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Is this a calculus class? You should be VERY familiar with \(\displaystyle x(t) = a(t)\cdot\;t^{2} + v_{0}\cdot\;t + x_{0}\)

a(t) may be constant.

...and it's 9.8 m/sec^2 -- Correct units will save you.
 
Hey i had this problem on my test today and couldnt figure out anyway to solve it since i dont have the base function
What do you mean by a "base" function?

4. A student is cleaning the outside of the patio windows at his aunt's apartment, which is located 90 meters above the ground. He accidentally kicks a flowerpot, sending it over the edge of the balcony.
This sets up something you learned back in algebra, and which was (almost certainly) reviewed in your calculus class; namely, projectile motion (in this case, of an object "projected" downward with an obvious initial velocity). To review, try here.

a) Determine an algebraic expression, in terms of a and h, to represent the average rate of change of the height above the ground of the falling flowerpot. Simplify your expression.
Plug the given info into the projectile-motion (height) equation. Then: What is the relationship between the height as a function of time, and the rate of change in the height with respect to time? If you had driven a certain distance over a certain period of time, what operation would you use to find the average rate of change in position (that is, the average rate of speed)?

b) Determine the average rate of change of the flowerpot's height above the ground in the interval between 1 second and 3 seconds after it fell from the edge of the balcony.
Evaluate the height equation at the specified values. Then use what you learned back in algebra ("d = rt") to find the average rate of change in position with respect to time.

c) Estimate the instantaneous rate of change of the flowerpot's height in 1 second and at 3 seconds.
We can't know what your book intends you to do when it tells you to "estimate". Please provide that information, and show how far you got in applying it.

d) Determine the equation of the tangent at t = 1. Sketch a graph of the curve and tangent at t = 1.
What is the relationship between a curve and the tangent to that curve at a specified point?

If you get stuck, please reply showing what you've tried, and your work and answers to the above questions. Thank you! ;)
 
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