To calculate the time it takes for the ball to reach a speed of 50 m/s, we can use the kinematic equation that relates initial velocity (u), final velocity (v), acceleration (a), and time (t):
v = u + at
where: v = final velocity (50 m/s) u = initial velocity (20 m/s) a = acceleration (we assume the acceleration due to gravity, which is approximately -9.81 m/s², since the ball is thrown downwards) t = time (what we want to find)
Let's rearrange the equation to solve for time (t):
t = (v - u) / a
Now, plug in the values:
t = (50 m/s - 20 m/s) / (-9.81 m/s²)
t = 30 m/s / -9.81 m/s²
t ≈ -3.06 seconds
The time is approximately -3.06 seconds. The negative sign indicates that the ball would take 3.06 seconds to reach a speed of 50 m/s in the downward direction after being thrown downwards with an initial speed of 20.0 m/s.