A bird sees a worm on the ground 50 m. below. The bird dives for the worm at a speed of 6 m/sec. The function h\left( t \right) = - 4.9{t^2} + 6t + 50h ( t ) = − 4.9 t 2 + 6 t + 50, where h(t) is the height of the bird at time t.

How long does the worm have before he is eaten? Round to the nearest tenth of a second.

Group of answer choices

1.9 seconds

3.9 seconds

12 seconds

4.9 seconds

Question

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Respuesta :

vijayalalitha vijayalalitha · Answer 1 · 2020-04-11T07:21:50+02:00

Given:

The height of the bird at time t is given by the function [tex]h(t)=-4.9t^2+6t+50[/tex]

We need to determine the time it takes the worm to be eaten by the bird.

Time taken:

The time can be determined by substituting h(t) = 0 in the function.

Thus, we have;

[tex]0=-4.9t^2+6t+50[/tex]

Switch sides, we get;

[tex]-4.9t^2+6t+50=0[/tex]

Let us solve the equation using the quadratic formula.

Thus, we get;

[tex]t=\frac{-6 \pm \sqrt{6^{2}-4(-4.9) 50}}{2(-4.9)}[/tex]

Simplifying, we get;

[tex]t=\frac{-6 \pm \sqrt{36+980}}{-9.8}[/tex]

[tex]t=\frac{-6 \pm \sqrt{1016}}{-9.8}[/tex]

[tex]t=\frac{-6 \pm 31.87}{-9.8}[/tex]

The values of t are given by

[tex]t=\frac{-6 + 31.87}{-9.8}[/tex] and [tex]t=\frac{-6 - 31.87}{-9.8}[/tex]

[tex]t=\frac{25.87}{-9.8}[/tex] and [tex]t=\frac{-37.87}{-9.8}[/tex]

[tex]t=-2.4[/tex] and [tex]t=3.9[/tex]

Since, the value of t cannot be negative, then [tex]t=3.9[/tex]

Thus, the time taken by the bird to eat the worm is [tex]t=3.9[/tex] seconds.

Hence, Option B is the correct answer.