The highest dive in the Olympic Games is from a 10-meter platform. The height "h" is in meters of a diver "t" seconds after leaving the platform can be estimated by the equation, h=10+4.9t-4.9t^2
I don't know how to make a successful table for this. I tried 0.1, 0.2, etc.. but that doesn't seem to work.
when t=.1 , h = 10 + 4.9(.1) - 4.9(.1)^2 =10.441
when t= .2 , h= 10 + 4.9(.2) - 4.9(.2)^2 = 10.784
what do you mean it "doesn't seem to work" ?
He clearly jumps upwards for a short time before his height decreases.
Just keep going the way I showed you.
The general equation for the height of an object falling from a height of H is
h = H - Vot - 9.8t^2/2 where H = the initial height in meters, Vo = the initial downward velocity in m/sec., 9.8 = the acceleration due to gravity in m/sec.^2 and t = the time to impact in seconds.
Your equation should therefore read
h=10-4.9t-4.9t^2, where I assume you have selected H = 10 and Vo as 4.9 m/s.
For t = .10, h = 10 - .49 - .049 = 9.461m.
For t = .20, h = 10 - .98 - .196 = 8.824m.
For t = .30, h = 10 - 1.47 - .441 = 8.089m.
t----.10----.20---.30------1.973
h...9.461..8.824..8.089.....10
To create a table for the equation, we can plug in different values for "t" and calculate the corresponding values for "h". Let's try using values in increments of 1 second to simplify the calculations:
When t = 0 seconds:
h = 10 + 4.9(0) - 4.9(0)^2
h = 10 + 0 - 0
h = 10
When t = 1 second:
h = 10 + 4.9(1) - 4.9(1)^2
h = 10 + 4.9 - 4.9
h = 10 + 0
h = 10
When t = 2 seconds:
h = 10 + 4.9(2) - 4.9(2)^2
h = 10 + 9.8 - 19.6
h = 10 - 9.8
h = 0.2
When t = 3 seconds:
h = 10 + 4.9(3) - 4.9(3)^2
h = 10 + 14.7 - 44.1
h = 10 - 29.4
h = -19.4
You can continue this process for as many values of "t" as desired.
To create a table for the given equation, you need to substitute different values of "t" into the equation and calculate the corresponding values of "h". Let's go step by step:
1. Start with a range of values for "t" that you want to use in your table. Since we are dealing with time after leaving the platform, it makes sense to start from zero seconds and go up to a few seconds. Let's say we choose t=0, 0.5, 1, 1.5, and 2 seconds.
2. Plug in each value of "t" into the equation h=10+4.9t-4.9t^2 and calculate the corresponding value of "h".
For t = 0 seconds:
h = 10 + 4.9(0) - 4.9(0)^2
= 10 + 0 - 4.9(0)
= 10
For t = 0.5 seconds:
h = 10 + 4.9(0.5) - 4.9(0.5)^2
= 10 + 4.9(0.5) - 4.9(0.25)
= 10 + 2.45 - 1.225
≈ 11.225
Continue the calculations for t = 1, 1.5, and 2 seconds.
3. Record the pairs of values (t, h) in a table.
t | h
---------------
0.0 | 10.0
0.5 | 11.225
1.0 | 10.1
1.5 | 6.675
2.0 | 1.6
So, based on the equation, the table of values for the height of the diver at different times would look like this:
t | h (height)
---------------
0.0 | 10.0
0.5 | 11.225
1.0 | 10.1
1.5 | 6.675
2.0 | 1.6
Now you have successfully created a table showing the estimated heights of the diver at different times after leaving the platform using the given equation.