Question

please help 10 points!!!

Answer 1

Answer:

2 seconds

Step-by-step 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.