Respuesta :

CastleRook
Time taken for the javelin to hit the ground will be given by:
A(t)=V'(t)=S''(t)
A(t)=-9.8m/s
⇒V(t)=-9.8t/1+C m/s

Where C is the initial velocity:
⇒V(t)=-9.8t+25
⇒S(t)=-9.8t²/2+25t/1+C
⇒S(t)=-4.9t²+25t+C
but the C is the initial vertical displacement, hence:
S(t)=-4.9t²+25t+1.6m

The time taken to hit the ground will therefore be:
S(t)=0
-4.9t²+25t+1.6=0

Using a quadratic function, it is found that it will take 5.17 seconds for the javelin to hit the ground.

What is the quadratic function for a projectile's height?

Considering meters as the measure of height, it is given by:

h(t) = -4.9t² + v(0)t + h(0).

In which:

  • v(0) is the initial velocity.
  • h(0) is the initial height.

In this problem, we have that v(0) = 25, h(0) = 1.6, hence:

h(t) = -4.9t² + 25t + 1.6

It hits the ground when h(t) = 0, hence:

-4.9t² + 25t + 1.6 = 0

4.9t² - 25t - 1.6 = 0.

Which is a quadratic function with coefficients a = 4.9, b = -25, c = -1.6. Hence:

[tex]\Delta = (-25)^2 - 4(4.9)(-1.6) = 656.36[/tex]

[tex]x_1 = \frac{25 + \sqrt{656.36}}{9.8} = 5.17[/tex]

[tex]x_2 = \frac{25 - \sqrt{656.36}}{9.8} = -0.06[/tex]

For time we want the positive value, hence, it will take 5.17 seconds for the javelin to hit the ground.

More can be learned about quadratic functions at https://brainly.com/question/24737967

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