quadratic applications

Question

When cannonballs are shot out of a cannon, their flight through the air depends on both the angle at which the cannon is set and the amount of gunpowder that is loaded into the cannon, which affects the initial velocity of the cannonball.

The equation y = 05r - 0.01r represents the parabola flight of a certain cannonball shot at an angle of 26° with the horizon and at an initial velocity of 25 meters per second. In this equation, y is the height of the cannonball, in meters, and a is the horizontal distance traveled, in meters The graph of the equation is shown to the right.

1.  Given that the points (10, 4) and (40, 4) lie on the parabola, at what x coordinate must the vertex Be?
2.  Use the equation and your answer to question 1 to find the maximum height of the cannonball.
3.  Use the point (0, 0) and the location of the vertex to find the total horizontal distance that the cannonball will travel.

When the angle of the cannon is decreased, the cannonball will travel in a different flight. The parabolic flight of the cannonball is shown to the right, with the vertex labeled.

4. What is the total horizontal distance that this cannonball will travel?

Using the same angle, the initial velocity of the cannonball is increased to produce the graph of the flight shown to the right. The point shown represents the total horizontal distance the cannonball will travel.

5. How far will the cannonball travel horizontally before it reaches its maximum height?

Answer 1

There is a flaw in the equation you've given to model the parabola. One of those r's should be squared. My guess is the first one, but you can confirm by rereading the problem where it was assigned to you.

1) see how these points both have the same y-value? This means you will find the vertex at the x-value that is halfway between those two points. (10+40)/2 plug this value into your corrected function for r to find the corresponding y-coordinate.

2) the y-value you found in 1 above is the maximum height in meters

3) this is asking you the change in x between the origin and the x-intercept after it

4) this is asking you a similar question to 3 above, but it sounds like not of the graph we've been using so far but a different one pictured in your text

5) the change in x between the origin and the vertex