Answer:
Hence, Grasshopper will land on the ground after 1.5 sec.
Step-by-step explanation:
It s given that:
The height, in feet, of the grasshopper above the ground after t seconds is modeled by the function:
[tex]h(t)=-t^2+\dfrac{4}{3}t+\dfrac{1}{4}[/tex]
Now we are asked to find:
In how many seconds will the grasshopper land on the ground?
i.e. we have to find the value of t such that h(t)=0
i.e.
[tex]-t^2+\dfrac{4}{3}t+\dfrac{1}{4}=0[/tex]
i.e. we need to find the roots of the given quadratic equation.
On solving the quadratic equation or plotting it's graph we could observe that the point where h(t)=0 are:
[tex]t=-\dfrac{1}{6},t=\dfrac{3}{2}[/tex]
As time can't be negative hence we will consider:
[tex]t=\dfrac{3}{2}=1.5sec[/tex]
Hence, grasshopper will land on the ground after 1.5 sec.
