Question

a bird is in a tree 30 feet off the ground and drops at Twigs at lands on a rose bush 25 ft below. the function h(t)=-16t^2+30, where T represents the time in seconds gifts the height H and feet of The Twig above the ground as it falls when will The Twig land on the bush

Answer 1

Answer: It will land on the bush after 1.25 seconds.

First, we will start with what we are given the equation: h(t) = -16t^2 + 30

Now, we should input a 5 for the h(t) because we want the seconds that will give us a height of 5 seconds.

5 = -16t^2 + 30

Solve the equation:
0 = -16t^2 + 25

To solve this, you could use the quadratic formula or factor out a -1 and you will have the difference of two squares.

Either way the answer is 1.25 seconds.

Answer 2

After 1.25 seconds the twig land on the bush.

Explanation:

Given function that shows the height of twig from the ground after t seconds,

`h(t)=-16t^2+30`

When twig is on the bush,

h(t) = 5 feet ( ∵ the distance from bush to ground = 30 - 25 = 5 feet )

`\implies -16t^2+30=5`

`-16t^2=-25`

`t^2=(25)/(16)`

`\implies t=\pm (5)/(4)`

Since, time can not be negative,

Hence, t =
`(5)/(4)` ≈ 1.25

Therefore, after 1.25 seconds the twig land on the bush.