A ball is kicked upwards the equation h(t)=-5t^2+40t describe the height in meters after t seconds. When you fill in the table don’t stop until the height is again at zero
Just finished at t = 1.234 got height = approx. 41.75 m
starting at t = 1.235
This is going to take forever!!
no table, but -5t^2+40t = -5t(t-8)
so h=0 at t=0 and at t=8
so keep going, and you'll finish up at
...
7.999 0.040
8.000 0.000
>whew<
To find the height of the ball after a given time, we can plug in the value of time (t) into the equation h(t) = -5t^2 + 40t.
Let's create a table to fill in the values of time and height. We'll start with a few values of t and calculate the corresponding height.
| t (seconds) | h(t) (meters) |
|-------------|--------------|
| 0 | |
| 1 | |
| 2 | |
| 3 | |
| 4 | |
| 5 | |
| 6 | |
| ... | |
We'll continue filling in the table until the height reaches zero again.
To fill in the value for t = 0, we substitute t = 0 in the equation: h(0) = -5(0)^2 + 40(0) = 0. So, when t = 0, the height is 0 meters.
Now, let's fill in the rest of the table by substituting the values of t into the equation:
| t (seconds) | h(t) (meters) |
|-------------|----------------------|
| 0 | 0 |
| 1 | -5(1)^2 + 40(1) |
| 2 | -5(2)^2 + 40(2) |
| 3 | -5(3)^2 + 40(3) |
| 4 | -5(4)^2 + 40(4) |
| 5 | -5(5)^2 + 40(5) |
| 6 | -5(6)^2 + 40(6) |
| ... | |
You can continue filling in the table by substituting the values of t and calculating the corresponding height using the equation. Keep filling in the values until the height reaches zero again.