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The formula h = -4.9t2...

1. A fire hose shoots water into the air from the ground. The formula h = -4.9t2 + 7t gives the height in meters t seconds after leaving the ground. This motion is called projectile motion and the path is the same as a cannon ball shot out of a cannon or a baseball thrown in the air at 7 meters per second could follow.

a.Does the graph of this equation resemble a U or an upside down U? How did you determine this?

b.Describe what happens the height as time passes?

c.Use the method of your choice to find how long it takes water to travel from the tip of the hose back to the ground.

d.Will the height peak or be at a low during the middle of the time the water is in the air? How do you know?

e.After how many seconds will the peak or low occur?

f.How high will the water be when the peak or low occurs?

g.What are the coordinates of the vertex? How does this number relate to your answers in parts e and f?

h.How many solutions are there to the equation 0 = -4.9t2 + 7t? How do you know?

i.To use the quadratic formula to solve an equation like this, we need three values, represented in your text by a, b and c. In the equation in part h, what are a, b & c?

j.What do the solutions represent? Is there a solution that does not make sense? If so, in what ways does the solution not make sense?

If there is a part a-j that you could not answer, you may use the following as an alternative. This part will only count if you skip one of the above parts and note that you are using the alternative.

Sketch the parabola represented by the equation h = -4.9t2 + 7t for the part of the parabola where h>0.

2. To stabilize a rectangular wooden gate, it is common practice to put a diagonal brace across the gate.

a. The width of the gate is 3 feet larger than the height. If the diagonal brace measures 3√5 feet, what are the width and height of the gate? Express your answer in feet and inches; round to the nearest inch.

b. If the width of the gate is 116 inches and the height is half of the width, how long would the diagonal brace need to be? Round your answer to the nearest inch.

a.Does the graph of this equation resemble a U or an upside down U? How did you determine this?

b.Describe what happens the height as time passes?

c.Use the method of your choice to find how long it takes water to travel from the tip of the hose back to the ground.

d.Will the height peak or be at a low during the middle of the time the water is in the air? How do you know?

e.After how many seconds will the peak or low occur?

f.How high will the water be when the peak or low occurs?

g.What are the coordinates of the vertex? How does this number relate to your answers in parts e and f?

h.How many solutions are there to the equation 0 = -4.9t2 + 7t? How do you know?

i.To use the quadratic formula to solve an equation like this, we need three values, represented in your text by a, b and c. In the equation in part h, what are a, b & c?

j.What do the solutions represent? Is there a solution that does not make sense? If so, in what ways does the solution not make sense?

If there is a part a-j that you could not answer, you may use the following as an alternative. This part will only count if you skip one of the above parts and note that you are using the alternative.

Sketch the parabola represented by the equation h = -4.9t2 + 7t for the part of the parabola where h>0.

2. To stabilize a rectangular wooden gate, it is common practice to put a diagonal brace across the gate.

a. The width of the gate is 3 feet larger than the height. If the diagonal brace measures 3√5 feet, what are the width and height of the gate? Express your answer in feet and inches; round to the nearest inch.

b. If the width of the gate is 116 inches and the height is half of the width, how long would the diagonal brace need to be? Round your answer to the nearest inch.

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