Answer:
[tex]t \approx 0.43\,s[/tex]
Step-by-step explanation:
The vertical displacement function is [tex]y(t) = -4.9\cdot t^{2}-3.5\cdot t + 2.4[/tex], where [tex]y(t)[/tex] is measured in meters and [tex]t[/tex] in seconds. Ball hits the ground when [tex]y(t) = 0[/tex]. That is:
[tex]-4.9\cdot t^{2}-3.5\cdot t + 2.4 = 0[/tex]
Whose roots can be found by using the General Formula for Second-Order Polynomials:
[tex]t_{1,2} = \frac{3.5\pm \sqrt{(-3.5)^{2}-4\cdot (-4.9)\cdot (2.4)} }{2\cdot (-4.9)}[/tex]
Solutions of this polynomial are:
[tex]t_{1} \approx 0.43\,s,t_{2} \approx -1.14\,s[/tex]
Only the first root is physically consistent.
