Calculating Melon Coordinates on a Parabolic Bank: A Physics Problem"

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In summary, a truck loaded with cannonball watermelons stops suddenly to avoid running over the edge of a washed-out bridge. One melon rolls off the truck with an initial speed of 8.0 m/s in the horizontal direction. The bank has the shape of a bottom half of a parabola with the equation y^2 = 14x. The x and y coordinates of the melon when it splatters on the bank can be found by finding the point where the path of the melon intersects with the bank.
  • #1
Sunnie
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A truck loaded with cannonball watermelons stops suddenly to avoid running over the edge of a washed-out bridge (see figure). The quick stop causes a number of melons to fly off the truck. One melon rolls over the edge with an initial speed vi = 8.0 m/s in the horizontal direction. A cross-section of the bank has the shape of the bottom half of a parabola with its vertex at the edge of the road, and with the equation y2 = 14x, where x and y are measured in meters. What are the x and y coordinates of the melon when it splatters on the bank?

How do you find the angle out of Y2=14x?
 
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  • #2
Sunnie said:
A truck loaded with cannonball watermelons stops suddenly to avoid running over the edge of a washed-out bridge (see figure). The quick stop causes a number of melons to fly off the truck. One melon rolls over the edge with an initial speed vi = 8.0 m/s in the horizontal direction. A cross-section of the bank has the shape of the bottom half of a parabola with its vertex at the edge of the road, and with the equation y2 = 14x, where x and y are measured in meters. What are the x and y coordinates of the melon when it splatters on the bank?

How do you find the angle out of Y2=14x?

why would you want to find an angle? You just want an equation for the path that the
water melon will follow, and combine that with y^2 = 14x to get the point where that path
will intersect with the bank
 
  • #3


To find the angle, we can use the equation tanθ = y/x, where θ is the angle, y is the vertical distance, and x is the horizontal distance. In this case, the vertical distance is given by the height of the bank, which is the y coordinate of the melon when it splatters (since it is at the same level as the bank). The horizontal distance is given by the x coordinate of the melon when it splatters. So we can rearrange the equation to solve for θ: θ = arctan(y/x).

First, we need to find the x coordinate of the melon when it splatters. To do this, we can use the equation of the parabolic bank, y2 = 14x, and substitute in the initial velocity of the melon vi = 8.0 m/s for y. This gives us the equation (8.0 m/s)2 = 14x, which we can solve for x to get x = 4.0 m.

Now that we have the x coordinate, we can use it to find the y coordinate using the equation of the parabolic bank again. Substituting in x = 4.0 m, we get y2 = 14(4.0 m), which gives us y = 6.0 m.

Therefore, the coordinates of the melon when it splatters on the bank are (4.0 m, 6.0 m).

It is important to note that the angle found using the equation tanθ = y/x represents the angle at which the melon hits the bank. This angle can be used to calculate the force of impact and other factors related to the physics of the problem.
 

1. What does "can't find the angle" mean?

"Can't find the angle" refers to the difficulty in determining or measuring the angle of a geometric shape or object.

2. Why is it important to find the angle?

Finding the angle is crucial in many mathematical and scientific applications, such as calculating distances, determining the shape of a structure, or predicting the trajectory of an object.

3. What are some common techniques for finding angles?

Some common techniques for finding angles include using a protractor, measuring with a ruler, using trigonometric functions, and applying geometric principles such as the Pythagorean theorem.

4. What can I do if I can't find the angle?

If you are having trouble finding the angle, try using multiple methods to confirm your measurement. You can also seek help from a teacher or consult online resources for step-by-step guidance.

5. Are there any tools or software that can help me find angles?

Yes, there are many tools and software available that can assist in finding angles. Some examples include angle finders, angle measuring apps, and online calculators. However, it is important to understand the principles behind these tools to ensure accurate results.

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