Answer:
t = 5 seconds
Step-by-step explanation:
We must solve the equation of movement of the ball as a function of time in seconds.
We must find how many seconds it takes until the ball touches the ground. When the ball touches the ground, the height b (t) = 0
Then we equate the equation to zero and solve for t.
[tex]80t-16t ^ 2 + 3.5 = 0[/tex]
Use the quadratic formula.
Where
[tex]a = -16\\\\b = 80\\\\c = 3.5[/tex]
[tex]t = \frac{-b \±\sqrt{b^2-4ac}}{2a}\\\\\\t_1 = \frac{-(80)-\sqrt{(80)^2-4(-16)(3.5)}}{2(-16)}\\\\t_1= 5.04\ s\\-------------------------\\t_2 =\frac{-(80)+\sqrt{(80)^2-4(-16)(3.5)}}{2(-16)}\\\\t_2=-0.0434\ s[/tex]
We take the positive solution
t = 5 seconds
