Final answer:
To find the initial velocity of the ball relative to the quarterback, we need to calculate both the horizontal and vertical components of the velocity. Using trigonometry, we can find the vertical velocity and calculate the time of flight. By combining the horizontal velocity and the time of flight, we can determine 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 it down 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° relative to the ground, so we can use trigonometry to find its vertical velocity. The initial 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.
Given that the ball is caught at the same height as it was released, the final vertical displacement is 0.
Using the equation y = v0yt + 0.5at2, where y is the vertical displacement, a is the acceleration due to gravity (9.8 m/s2), and t is the time, we can solve for the time of flight.
Now we can use the time of flight and the horizontal velocity to find the horizontal displacement using the equation x = v0x * t.
Putting it all together, we can calculate the initial velocity of the ball relative to the quarterback.