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

[Sunnie]

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?

 

[kamerling]

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

 

[Moetasim]

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.