Hey guys i have a little assignment for you guys to do. My students have had a tough time doing this and i wanted to see if any of you can get this right.The first person to get this correct i will help them with any math related problems for a week. Good luck
Activity 1: Graphing
An archer releases an arrow at shoulder height.
• Measure the distance from the floor to your shoulder when you are standing.
Suppose you release an arrow and it hits the target at a point 5 ft above the
ground. Sketch a possible parabolic path of your arrow’s fl ight using this
information.
Archery is one of only a few sports in which athletes using wheelchairs can
compete with other athletes.
• Measure the distance from the fl oor to your shoulder while you are sitting
in a chair. Sketch the possible path of an arrow released by someone using a
wheelchair.
• Describe the similarities and differences between your two sketches.
Activity 2: Analyzing
An archer releases an arrow from a shoulder height of 1.39 m. When
the arrow hits the target 18 m away, it hits point A. When the target is
removed, the arrow lands 45 m away. Find the maximum height of the
arrow along its parabolic path.
Activity 3: Modeling
Archers need to use arrows that do not bend easily. Th e table shows how the weight of
an arrow affects its spine, or the distance the center of the arrow bends when a certain
constant weight is attached. Graph the data in the table to find a linear and a quadratic
model for the data. Use the regression feature on your calculator to find each model.
Which model is a better fit? Explain.
This is a joke, first off a teacher never says I will help you for a week, they should help you all the time...second off, we won't do your homework!
Another thing is that,
1. Teachers put I not i.
2. This is the same assignment that Connections Academy is having their students do..
To answer Activity 1: Graphing, you will need to sketch the possible parabolic paths of an arrow's flight in two different scenarios - when released from a standing position and when released from a sitting position in a wheelchair.
1. Measure the distance from the floor to your shoulder when standing. This measurement will give you a starting point for the parabolic path.
2. Suppose the arrow hits a point 5 ft above the ground. Start your sketch from the measurement taken in step 1 and draw a parabolic curve going upwards, reaching a maximum height of 5 ft above the ground, and then descending towards the target.
3. For the second scenario, measure the distance from the floor to your shoulder while sitting in a wheelchair. This measurement will give you a new starting point for the parabolic path.
4. Sketch a new parabolic curve starting from the measurement taken in step 3, going upwards, reaching a maximum height, and then descending towards the target.
5. Compare the two sketches and describe the similarities and differences between them. Consider factors such as the starting point, maximum height, and general shape of the curves.
To answer Activity 2: Analyzing, you need to find the maximum height of the arrow along its parabolic path, given the release height and the distances traveled by the arrow.
1. The archer releases the arrow from a shoulder height of 1.39 m.
2. When the arrow hits the target 18 m away, it reaches point A.
3. When the target is removed, the arrow lands 45 m away.
4. Use the distance and height information to set up two equations:
a) Using the equation for the horizontal distance, we can write: 18 = d + 45, where d is the horizontal distance between point A and the landing point without the target.
b) The maximum height occurs when the projectile is halfway between the release point and the landing point without the target. So the horizontal distance at the maximum height, x, will be (18 + 45)/2 = 31.5 m.
c) Using the equation for vertical motion, we can write: H = h + x * tan(theta) - (g * x^2) / (2 * v^2 * cos^2(theta)), where H is the maximum height, h is the release height, x is the horizontal distance at the max height, theta is the angle of projection, g is the acceleration due to gravity, and v is the initial velocity.
5. Substitute the known values into the equation from step 4c and solve for H, the maximum height of the arrow along its parabolic path.
To answer Activity 3: Modeling, you need to graph the data in the table and find a linear and a quadratic model using regression analysis.
1. Create a scatter plot with the arrow weight on the x-axis and the spine distance on the y-axis.
2. Using a graphing calculator or statistical software, perform a regression analysis to find both a linear and a quadratic model for the data.
3. Compare the goodness of fit for both models by looking at the correlation coefficient (R^2) values. A higher R^2 value indicates a better fit.
4. Explain which model is a better fit based on the R^2 values. If the quadratic model has a higher R^2 value, it means that the quadratic model is a better fit for the given data. Explain why the chosen model fits the data better, considering factors such as the curvature of the data points.