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So I have received my semester math project for my Adv. Algebra II class. Here it is:

The Thunder Aeronautical Toy Company (TATC) has hired you as a mathematical consultant for their new project. They are designing a TIE fighter that will launch straight up intot he air and fall back down to the ground very close to the launch pad. They have determined that the following formula can be used to calculate the height (h) of the TIE Fighter at any given time(t):

.. Where V

TATC has hired you, the mathematical guru, to help them determine certain criteria of their toy. The questions they need answered are:

1.) If TATC designed an engine to give an initial velocity of 30 m/s, what would be the maximum height the TIE Fighter would achiece? 40 m/s? 50 m/s?

3.) If the initial velocity was 30 m/s, how long would the TIE Fighter be in the air? 40 m/s? 50 m/s?

4.) What if TATC wanted the TIE Fightert o be in the air for 15s, at what initial velocity would their engineers need to design the engine?

One, two, and four are all extremely easy to figure out. It's two that I'm having trouble on.

I wrote the equation as such:

Which I know is right, it's just that I'm not sure what other equation I could form from this problem to potentially set to this one and solve for one of the unknown variables ( V

I cannot use physics equations in this problem. Only algebra II knowledge. I already figured it out with a physics equation, I just can't get it through algebra only.

I don't want the answer, only some advice on where to start, if anyone would be so kind.

Thanks a bunch~

The Thunder Aeronautical Toy Company (TATC) has hired you as a mathematical consultant for their new project. They are designing a TIE fighter that will launch straight up intot he air and fall back down to the ground very close to the launch pad. They have determined that the following formula can be used to calculate the height (h) of the TIE Fighter at any given time(t):

**h = (V**_{0})(t) - (.5)(g)(t^{2}).. Where V

_{0}= initial velocity (speed) and g = 9.8 m/s^{2}(gravity).TATC has hired you, the mathematical guru, to help them determine certain criteria of their toy. The questions they need answered are:

1.) If TATC designed an engine to give an initial velocity of 30 m/s, what would be the maximum height the TIE Fighter would achiece? 40 m/s? 50 m/s?

**2.) What initial velocity would give a maximum height of 100m?**3.) If the initial velocity was 30 m/s, how long would the TIE Fighter be in the air? 40 m/s? 50 m/s?

4.) What if TATC wanted the TIE Fightert o be in the air for 15s, at what initial velocity would their engineers need to design the engine?

One, two, and four are all extremely easy to figure out. It's two that I'm having trouble on.

I wrote the equation as such:

**100m = V**_{0}t - .5(9.8)t^{2}Which I know is right, it's just that I'm not sure what other equation I could form from this problem to potentially set to this one and solve for one of the unknown variables ( V

_{0}and t ).I cannot use physics equations in this problem. Only algebra II knowledge. I already figured it out with a physics equation, I just can't get it through algebra only.

I don't want the answer, only some advice on where to start, if anyone would be so kind.

Thanks a bunch~

**EDIT : SOLVED. WOOO.**
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