Question

Need Help:
Please show ALL work and tell me which method you used (quadratic, completing the square, etc.)

1.) A flare is fired straight up from the ground with an initial velocity of 100 feet per second. How long will it take for the flare to reach an altitude of 150 feet?

2.) A flare is fired straight up from the ground with an initial velocity of 100 feet per second. How long will it take for the flair to reach an altitude of 175 feet?

Answer 1

Hi! Are you aware of the formula:\[h = v_it- \dfrac{1}{2}gt^2\]

Answer 2

It's the second equation of a motion with constant acceleration.

Answer 3

Use the above formula, and plug in the following:

- The initial velocity is given as 100 feet/sec. Plug that in for \(v_i\).
- The height (altitude) is given as 150 feet. Plug that in for \(h\).

You will get a quadratic equation in \(t\), more or less.

Answer 4

Of course, use the value of \(g\) you are given.

Answer 5

The problem that I have with these two question is that every method that I try to use, I always get two answers....which is impossible, however there not being an answer is also impossible. So can you walk me through step by step for at least the first one?

Answer 6

Whenever a formula has a "squared" term (²), there is always going to be two answers.
Example:
What is the square root of 16?

Answer 7

You can get two answers. It makes sense. If you throw a ball up, it's going to end up at the same point at two different times: one, when it is going up, and the second, when it's going down.

Answer 8

So then do I do the lowest one for the answer, or do I write them both down.

Answer 9

Both of them. But assure that time is not negative.