Final answer:
To find the initial velocity of the ball relative to the quarterback, we need to break down the motion into horizontal and vertical components. By using trigonometry and equations for vertical and horizontal velocity, we can find the initial velocity of the ball relative to the quarterback.
Step-by-step explanation:
To find the initial velocity of the ball relative to the quarterback, we can break down the motion into horizontal and vertical components. The quarterback is moving straight backward, so his horizontal velocity is -2.00 m/s. The ball is thrown at an angle of 25.0°, and we can use trigonometry to find its vertical and horizontal velocities.
Vertical component: The vertical velocity can be found using the equation v = v0sinθ, where v is the vertical velocity, v0 is the initial velocity, and θ is the angle of projection. In this case, the initial vertical velocity is v0y = v0sin(25.0°).
Horizontal component: The horizontal velocity remains constant throughout the motion, so the horizontal velocity of the ball is equal to the horizontal velocity of the quarterback, which is -2.00 m/s.
Therefore, the initial velocity of the ball relative to the quarterback can be found by combining its vertical and horizontal velocities, resulting in an initial velocity of v0 = √(v0x2 + v0y2).