Question

Please help 10 points!!!

Answer 1

2 seconds

Explanation:

The variable S represents the height off the ground, so we can substitute in the value 140 for it:

`140 = 80t - 5t^(2)`

We can add
`5t^(2)` to both sides and subtract
`80t` so the equation is in standard form:

`5t^(2) - 80t + 140 = 0`

Every term has five as a factor, so we may divide both sides of the equation by 5.

`t^(2) - 16t + 28 =0`

To factor this, we need two numbers that multiply to 28 and sum to -16. These numbers are -14 and -2, so these are the two factors:

`(t-14)(t-2)=0`

We can see that when t = 14 or 2, the whole left has a value of zero, so they are the two answers.

We are asked when the rocket first is at 140m, and 2 seconds is before 14, so the answer is 2 seconds.