To find the football's overall velocity and direction, we can use vector addition. The horizontal and vertical velocities can be combined to find the resultant velocity.
Given: Horizontal velocity (Vx) = 15.0 m/s (in the positive x-direction) Vertical velocity (Vy) = 4.25 m/s (in the positive y-direction)
Using the Pythagorean theorem, we can find the magnitude (or speed) of the resultant velocity (V) as follows:
V = √(Vx^2 + Vy^2)
V = √(15.0^2 + 4.25^2) V = √(225 + 18.0625) V = √243.0625 V ≈ 15.59 m/s
The magnitude of the football's velocity is approximately 15.59 m/s.
To determine the direction, we can use trigonometry. The angle (θ) between the resultant velocity vector and the positive x-axis can be found using the following equation:
θ = arctan(Vy / Vx)
θ = arctan(4.25 / 15.0) θ ≈ 16.69 degrees
Therefore, the football's velocity is approximately 15.59 m/s at an angle of 16.69 degrees above the positive x-axis.