Question

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

Answer 1

Given:

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

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;

`0=-4.9t^2+6t+50`

Switch sides, we get;

`-4.9t^2+6t+50=0`

Let us solve the equation using the quadratic formula.

Thus, we get;

`t=\frac{-6 \pm \sqrt{6^(2)-4(-4.9) 50}}{2(-4.9)}`

Simplifying, we get;

`t=(-6 \pm √(36+980))/(-9.8)`

`t=(-6 \pm √(1016))/(-9.8)`

`t=(-6 \pm 31.87)/(-9.8)`

The values of t are given by

`t=(-6 + 31.87)/(-9.8)` and
`t=(-6 - 31.87)/(-9.8)`

`t=(25.87)/(-9.8)` and
`t=(-37.87)/(-9.8)`

`t=-2.4` and
`t=3.9`

Since, the value of t cannot be negative, then
`t=3.9`

Thus, the time taken by the bird to eat the worm is
`t=3.9` seconds.

Hence, Option B is the correct answer.