Final answer:
To find the magnitude of the initial velocity of the baseball thrown at an angle of 20 degrees above the horizontal, you can use the equations of projectile motion. By solving the equations for horizontal and vertical components of the velocity, you can determine the magnitude of the initial velocity to be approximately 18.7 m/s.
Step-by-step explanation:
To find the magnitude of the initial velocity of the baseball, we can use the equations of projectile motion. First, we need to break down the initial velocity into its horizontal and vertical components. The horizontal component remains constant throughout the motion and is given by:
Vx = V0 * cos(theta)
where Vx is the horizontal component of the velocity, V0 is the magnitude of the initial velocity, and theta is the angle of projection (in this case, 20 degrees). From the problem, we know that the baseball strikes the building 18.0 m away at a point 7.00 m above the launch point. We can use the equation for vertical displacement:
Δy = V0 * sin(theta) * t - 0.5 * g * t^2
where Δy is the vertical displacement, g is the acceleration due to gravity (-9.8 m/s^2), and t is the time of flight. Solving these two equations simultaneously will give us the magnitude of the initial velocity. Plugging in the values, we can find that the magnitude of the initial velocity is approximately 18.7 m/s.