Question

A grasshopper jumps off a tree stump. The height, in feet, of the grasshopper above the ground after t seconds is modeled by the function shown.
h(t) = -t² + 4/3t + 1/4

After how many seconds will the grasshopper land on the ground?

Answer 1

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:

$h(t)=-t^2+\dfrac{4}{3}t+\dfrac{1}{4}$

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.

$-t^2+\dfrac{4}{3}t+\dfrac{1}{4}=0$

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:

$t=-\dfrac{1}{6},t=\dfrac{3}{2}$

As time can't be negative hence we will consider:

$t=\dfrac{3}{2}=1.5sec$

Hence, grasshopper will land on the ground after 1.5 sec.