A.B.
A ball is launched from the ground and reaches a height of 60 meters and returns to the ground in 5 seconds. In this application i will be looking for the exact velocity of the ball at 1 second.
the table looks like this......
T0=0; T1=38; T2=56; T3=58; T4=36
T0=0; T1=38; T2=56; T3=58; T4=36
My three lines will be from 1 to 4 sec, 1 to 3 sec, and 1 to 2 sec. So my points are (1, 36), (1, 58), (1,56) all originating from (1,38)..... So the ARC from one to two seconds is 56-38 = 18 2-1
from two to three seconds is 58-56 = 2 from three to four seconds is 36-58 = -22 or 22
3-2 4-3
The mean/average rate of change is 14. Where as the rate of change of the three secant lines is....
56-38=18 58-38=20 36-38= -2 the mean of these numbers is 12.
the rate of change between 0 and 1 second is 38 and from 1 to 2 seconds is 18. so to find the instantaneous rate of change at one second we know that the rate of change is between 38 and 18 meters per second because the velocity of the ball is always changing.
This being said, the IRC at one second is 28 meters per second.
The Tangent line would look like the following...
So 1=38 and .5=20 So the slope is 18/.5 for the point at t=1
Your blog is clearly written and the calculations were easy to follow. I very much appreciated your graphs that you had on your blog, it added to giving me a visual. It is cool to know that a ball can travel 28 meters per second when tossed.
ReplyDeleteYour answers are well organized, but I think including the letters for the corresponding question could have made it easier to follow. Your graphs are neat and easy to read and overall it looks like you did a good job!
ReplyDeleteReally liked the use of the graphs- very clear and easy to follow!
ReplyDeleteShannon, nice job on the visual aids! You also did a good job keeping everything.g organized. Most of your calculations are correct. But your secant line calculations should be 18, 10, -2/3, because 56 - 38/ 2-1, 58-38/3-1, and 36- 38/4-1. You do come
ReplyDeleteto the conclusion that the rates of change are increasing, so that's good. Some of your explanations could have been more detailed, but other than that, good job. 😁