Final answer:
To find the initial speed of the soccer ball, we can use the principles of projectile motion. The correct answer is 16.5 m/s.
Step-by-step explanation:
To find the initial speed of the soccer ball, we can use the principles of projectile motion. The vertical component of the initial velocity can be found using the equation vf = vi + gt, where vf is the final vertical velocity (0 m/s at the top of the goal), vi is the initial vertical velocity, g is the acceleration due to gravity (9.8 m/s^2), and t is the time taken to reach the top of the goal.
The height of the goal is 2.44 m, so we can use the equation y = vi * t - 0.5 * g * t^2 to find t. Plugging in the values, we get 2.44 = vi * t - 0.5 * 9.8 * t^2. Rearranging and solving for t, we get a quadratic equation 4.9t^2 - vit + 2.44 = 0.
Using the quadratic formula, we can solve for t, and then substitute the value of t into the equation vf = vi + gt to find vi. The initial speed of the soccer ball is approximately 16.5 m/s, so the correct answer is a) 16.5 m/s.