Question

(a) How high is the javelin when it was thrown? How do you know?(b) How far from the thrower does the javelin strike the ground?

Answer 1

The height of the javelin is given by

`h(x)=-(1)/(20)x^2+8x+6`

Here, x is the horizontal distance from the point at which the javelin is thrown.

a)

When the javelin is thrown, the horizontal distance from the point at which the javelin is thrown is zero. So, put x = 0 to find the height of the javelin when thrown. So, the distance:

`\begin{gathered} h(0)=-(1)/(20)(0)^2+8(0)+6 \\ =0+0+6 \\ =6 \end{gathered}`

Thus, the height of the javelin when it was thrown is 6 ft.

b)

When the javelin strikes the ground the value of h(x) is zero.

Find the value of x when h(x) is zero.

`\begin{gathered} h(x)=0 \\ -(1)/(20)x^2+8x+6=0 \\ -x^2+160x+120=0 \\ x^2-160x-120=0 \end{gathered}`

Now, the roots of the equation are x = 160.74 and x = -0.74.

The distance cannot be negative. So, the javelin is 160.74 ft far from the thrower when it strikes the ground.