Final answer:
The ball was thrown from a height of approximately 26.61 meters. This was calculated using the horizontal motion to find the time the ball was in the air and then using the vertical motion equation to find the height.
Step-by-step explanation:
To determine from what height the ball was thrown, we need to calculate the time it took for the ball to hit the ground based on the horizontal motion and then use this time to find the vertical distance it fell due to gravity. Since the ball was thrown horizontally, the vertical velocity initially is 0 m/s. We use the kinematic equation for constant acceleration, where the horizontal distance (d) is equal to the horizontal velocity (v) multiplied by time (t): d = vt. Rearranging for t gives us t = d/v.
For the horizontal motion:
d = 56.0 m
v = 24.0 m/s
t = 56.0 m / 24.0 m/s = 2.333 s (approximately)
Now, we use the vertical motion to find the height (h), where the vertical distance is due to the gravitational acceleration (g = 9.8 m/s^2). The equation for vertical motion is h = 1/2gt^2:
h = 1/2 × 9.8 m/s^2 × (2.333 s)^2
h = 1/2 × 9.8 m/s^2 × 5.44 s^2
h = 26.61 m
Therefore, the ball was thrown from a height of approximately 26.61 meters.