Final answer:
The speed of the ball after it has traveled 4.20 m downward is approximately 24.04 m/s.
Step-by-step explanation:
To calculate the speed of the ball after it has traveled 4.20 m downward, we need to use the principles of free fall and the equations of motion. Since the ball is dropped from a height of 55.0 m, we can calculate the initial velocity using the equation v_i = sqrt(2 * g * h), where v_i is the initial velocity, g is the acceleration due to gravity (9.8 m/s^2), and h is the height (55.0 m). Plugging in these values, we find that the initial velocity is approximately 34.02 m/s.
Next, we can calculate the final velocity using the equation v_f = sqrt(v_i^2 + 2 * g * d), where v_f is the final velocity, v_i is the initial velocity, g is the acceleration due to gravity, and d is the distance traveled downward (4.20 m). Plugging in the values, we get v_f = sqrt((34.02 m/s)^2 + 2 * (9.8 m/s^2) * (4.20 m)) = approximately 24.04 m/s.
Therefore, the speed of the ball after it has traveled 4.20 m downward is approximately 24.04 m/s.