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

1.5 sec

Explanation:

:D

Answer 2

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

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+(4)/(3)t+(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+(4)/(3)t+(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=-(1)/(6),t=(3)/(2)`

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

`t=(3)/(2)=1.5sec`

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