Final answer:
To find the height from which the ball was thrown, we calculate the time it was airborne using the horizontal travel distance and initial speed, then apply the kinematic equation for vertical distance traveled due to gravity, resulting in a height of approximately 21.0 meters.
Step-by-step explanation:
To calculate the height h from which the ball was thrown horizontally with a speed of vi = 27.0 m/s and travels a horizontal distance of d = 56.0 m before hitting the ground, we can use the equations of projectile motion. The time t it spends in the air is found using the horizontal motion equation: d = vi * t. The vertical motion then allows us to determine the height using the equation h = 0.5 * g * t2, where g is the acceleration due to gravity (approximately 9.81 m/s2).
First, we solve for t:
- d = vi * t
- 56.0 m = 27.0 m/s * t
- t = 56.0 m / 27.0 m/s
- t ≈ 2.074 s
Now we can find the height h using the vertical motion equation:
- h = 0.5 * g * t2
- h = 0.5 * 9.81 m/s2 * (2.074 s)2
- h ≈ 21.0 m
Therefore, the height from which the ball was thrown is approximately 21.0 meters.