Final answer:
To determine the height from which the ball was thrown, we find the time it was in the air using its horizontal distance and initial speed, and then use this to calculate the height using the vertical motion equation. The calculated height is approximately 21.0 meters.
Step-by-step explanation:
To find the height h from which a ball thrown horizontally with a speed of vi = 29.0 m/s travels a distance of d = 60.0 m before hitting the ground, we need to use the equations of motion for projectile motion. Since the horizontal and vertical motions are independent, we can analyze them separately.
Firstly, we use the equation for the horizontal motion to figure out how long the ball is in the air. The horizontal speed is constant, so Time (t) = d / vi. Substituting the known values, we get t = 60.0 m / 29.0 m/s, which equals approximately 2.07 seconds.
Next, for the vertical motion, we can use the second equation of motion: d = vit + (1/2)gt², where g is the acceleration due to gravity (9.81 m/s²) and vi is the initial vertical velocity (which is zero in the case of horizontal throw). Since the initial vertical velocity is zero, the equation simplifies to h = (1/2)gt².
Plugging in the values of g and t, we get h = (1/2)(9.81 m/s²)(2.07 s)², which equals approximately 21.0 meters. Therefore, the ball was thrown from a height of about 21.0 meters above the ground.