Zech tossed a water balloon into the air from the top of his shed in the backyard. Use GeoGebra to graph the situation using the formula y=−6t2+30t+8
. When will the balloon hit the ground? Round your answer to the nearest tenth of a second.(1 point)
The balloon will hit the ground at
seconds.
To graph the situation using the formula y = -6t^2 + 30t + 8 on GeoGebra, we need to plot the values of y for different values of t.
1. Open GeoGebra and go to the Algebra view.
2. In the input bar, type y = -6t^2 + 30t + 8 and press Enter.
3. Now, we need to specify the range of t values. Click on the icon "Sequence" on the toolbar.
4. In the dialog box that appears, enter the following values:
- Name: t
- Start: 0
- End: 5
- Step: 0.1
5. Click on the "OK" button.
6. In the input bar, type y(t) to display the values of y corresponding to the t values we specified.
7. A table will appear showing the values of t and y.
8. To visualize the graph, click on the icon "Graphics View" on the toolbar.
9. In the input bar, type Sequence(t,y) and press Enter.
10. The graph of the situation will be displayed in the Graphics view.
To find out when the balloon hits the ground, we need to look for the value of t when y = 0.
11. In the input bar, type t(y=0) and press Enter.
12. The output will be the value of t when the balloon hits the ground, rounded to the nearest tenth of a second.
how many seconds will the ballon take to hit the ground
To determine the number of seconds it will take for the balloon to hit the ground, we need to find the value of t when y = 0.
Using the equation y = -6t^2 + 30t + 8, we can set y to 0 and solve for t:
0 = -6t^2 + 30t + 8
To solve this quadratic equation, we can use the quadratic formula:
t = (-b ± √(b^2 - 4ac)) / (2a)
In this case, a = -6, b = 30, and c = 8.
Plugging these values into the formula:
t = (-30 ± √(30^2 - 4*(-6)*(8))) / (2*(-6))
Simplifying the equation:
t = (-30 ± √(900 + 192)) / (-12)
t = (-30 ± √1092) / (-12)
Now we can calculate the values for t:
t1 = (-30 + √1092) / (-12) ≈ 4.7
t2 = (-30 - √1092) / (-12) ≈ -0.4
Since time cannot be negative in this context, we can disregard the negative value and conclude that the balloon will hit the ground at approximately 4.7 seconds.