Question

15. JAGUARUNDI A jaguarundi springs from a fence post to swat at a low flying bird.

Answer 1

Answer:

The discriminant, -14.71 < 0, shows that there is no solution of the equation, h = -16·t² + 22.3·t + 2, at the line 'h = 10' feet, therefore, the Jaguarundi height as she springs will not be up to 10 feet and therefore she will not reach the bird

Step-by-step explanation:

From the question, the equation that models the Jaguarundi's height, 'h', ma be written approximately as follows;

h = -16·t² + 22.3·t + 2

Where;

t = The time (duration) in seconds

The discriminant of the equation a·x² + b·x + c = 0 is  b² - 4·a·c

When h = 10, we have;

10 = -16·t² + 22.3·t + 2

∴ 0 = -16·t² + 22.3·t + 2 - 10 = -16·t² + 22.3·t - 8

The discriminant of the given quadratic equation is given as follows;

The discriminant = 22.3² - 4 × (-16 × (-8)) = -14.71 < 0

Therefore, the function, h = -16·t² + 22.3·t + 2 has no real root at h = 10

The parabola does not reach or pass through the line h = 10 which is the height at which the bird is flying.

The Jaguarundi will not reach the bird flying at the height of 10 feet.

Answer 2

Answer:

No, the Jaguarundi will not reach the bird

Step-by-step explanation:

The equation is

$h=-16t^2+22.3t+2$

When h = 10 feet

$10=-16t^2+22.3t+2$

$\Rightarrow -16t^2+22.3t-8=0$

$a=-16$

$b=22.3$

$c=-8$

Discriminant is given by

$b^2-4ac=22.3^2-4(-16)(-8)$

$\Rightarrow b^2-4ac=-14.71$

$\Rightarrow b^2-4ac$

So, the Jaguanrundi will not reach the bird as the roots will be imaginary.