To determine the maximum height reached by a ball thrown upwards with an initial speed of 20 m/s, we can use the equations of motion.
When the ball reaches its maximum height, its vertical velocity becomes zero. Using this information, we can find the time it takes for the ball to reach the highest point. The equation for the vertical velocity of an object in free fall is:
v = u + gt,
where: v is the final vertical velocity (0 m/s at the highest point), u is the initial vertical velocity (20 m/s in the upward direction), g is the acceleration due to gravity (-9.8 m/s², assuming Earth's gravity).
0 = 20 - 9.8t, 9.8t = 20, t = 20 / 9.8, t ≈ 2.04 seconds.
Now, we can use the time to find the maximum height reached by the ball. The equation for vertical displacement (height) is:
s = ut + (1/2)gt²,
where: s is the vertical displacement (height), u is the initial vertical velocity (20 m/s), t is the time (2.04 seconds), g is the acceleration due to gravity (-9.8 m/s²).
s = 20 * 2.04 + (1/2) * (-9.8) * (2.04)², s ≈ 20.4 meters.
Therefore, the maximum height reached by the ball is approximately 20.4 meters.