Question

If a rocket is propelled upward from ground level, its height in meters after t seconds is given by h= -9.8t^2 + 107.8t. During what interval of time will the rocket be higher than 294m ?

Answer 1

Answer:

$5$

Step-by-step explanation:

We know that the function of the height of a rocket after t seconds is:

$h(t)=-9.8t^2+107.8t$

We want to find the interval of time such that the rocket is higher than 294 meters.

So, substitute 294 for h(t) and solve for t:

$294=-9.8t^2+107.8t$

Just as it happens, everything is divisible by -9.8. So, divide everything by -9.8. This yields:

$-30=t^2-11t$

Add 30 to both sides:

$t^2-11t+30=0$

Factor. We can use -6 and -5. So:

$(t-6)(t-5)=0$

Zero Product Property:

$t-6=0\text{ or } t-5=0$

Solve for each equation:

$t=6\text{ or } t=5$

So, our answers are 5 seconds and 6 seconds.

Therefore, between the fifth and sixth second, the rocket is higher than 294 meters.

Note that at exactly the fifth and sixth second, our height is exactly 294 meters, not higher.

Therefore, we won't include 5 and 6 in our solution set.

As an inequality, this is:

$5$

In interval notation, this is:

$(5,6)$

And we're done!