XY coordinates of the right toe of a soccer kick performer are
Frame 20: (2.62, 0.99)
Frame 14: (2,34, 0.16).
How far did the toe travel in the upward direction between frames 14 and 20?
How fast did the toe travel in upward direction between frames 14 and 20?
How fast did the toe travel and in what direction between frames 14 and 20?
To answer these questions, we need to calculate the distance and speed of the toe's travel between frames 14 and 20. We will consider the upward direction as the y-axis.
1. To calculate the distance traveled in the upward direction between frames 14 and 20, we can use the formula for the distance between two points in a coordinate system. The formula is:
distance = √((x₂ - x₁)² + (y₂ - y₁)²)
Given coordinates:
Frame 20: (2.62, 0.99)
Frame 14: (2.34, 0.16)
Applying the formula:
distance = √((2.62 - 2.34)² + (0.99 - 0.16)²)
2. To calculate the speed of the toe's travel in the upward direction between frames 14 and 20, we need to divide the distance by the time interval. Unfortunately, the time interval is not provided. Without the time information, we cannot determine the exact speed.
3. To determine the toe's travel direction and speed between frames 14 and 20, we can calculate the displacement vector. The displacement vector is the difference between the final position and initial position. The direction can be described using the angle (θ) with the x-axis.
Given coordinates:
Frame 20: (2.62, 0.99)
Frame 14: (2.34, 0.16)
Calculate the displacement vector:
Δx = x₂ - x₁ = 2.62 - 2.34
Δy = y₂ - y₁ = 0.99 - 0.16
To find the direction:
θ = tan⁻¹(Δy/Δx)
To find the speed, we need to divide the magnitude of the displacement vector by the time interval. Without the time information, we cannot determine the exact speed.
Therefore, we can calculate the distance traveled in the upward direction between frames 14 and 20, but the speed and direction require time information.