Answer:
Step-by-step explanation:
We have been the model [tex]h(t) = 96t -16t^2[/tex]
Here. t is the time since launch and h(t) is the height in feet of the projectile after time t in seconds.
For the height of the object to be 144 feet, we have
[tex]h(t)=144\\\\96t -16t^2=144\\\\16t^2-96t+144=0\\\\\text{Using the quadratic formula, we get}\\\\t_{1,\:2}=\frac{-\left(-96\right)\pm \sqrt{\left(-96\right)^2-4\cdot \:16\cdot \:144}}{2\cdot \:16}\\\\t_{1,\:2}=\frac{-\left(-96\right)\pm \sqrt{0}}{2\cdot \:16}\\\\t=3[/tex]
Therefore, after 3 seconds the object will be 144 feet in the air.
Now, when the object hits the ground then the height should be zero.
[tex]96t -16t^2=0\\16t(6-t)=0\\t=0,6[/tex]
Hence, at t= 6 seconds, the object will hit the ground.
a. The time at which this object would be 144 feet in the air is 3 seconds.
b. The time it would take this object to hit the ground is 6 seconds.
Given the following data:
Where:
a. To determine when the object would be 144 feet in the air:
[tex]144 = 96t -16t^2\\\\16t^2-96t+144=0[/tex]
Dividing all through by 16, we have:
[tex]t^2-6t+9=0[/tex]
Solving the quadratic equation by factorization, we have:
[tex]t^2-3t-3t+9=0\\\\t(t-3)-3(t-3)=0[/tex]
t = 3 seconds.
b. To determine when the object would hit the ground:
Note: The object would would hit the ground when its height is zero (0).
[tex]96t-16t^2=0\\\\16(t-6)=0\\\\t-6=0[/tex]
t = 6 seconds.
Read more on time here: https://brainly.com/question/10545161
