Final answer:
To find the horizontal distance traveled by the ball, we first calculate the time it takes to fall from a 12 m height and then multiply this time by the constant horizontal speed. The time of fall is approximately 1.56 seconds, and the horizontal distance traveled is approximately 10.92 m, which is closest to option a) 10.5 m.
Step-by-step explanation:
The question involves determining the horizontal distance a ball will travel before hitting the ground after being thrown horizontally from a 12 m-high building at a speed of 7.0 m/s. To solve this, we only need to consider the vertical motion to find out how long it takes for the ball to hit the ground, since gravity acts only in the vertical direction and the horizontal speed remains constant (assuming air resistance is negligible).
To calculate the time of flight (t), we use the formula for the distance fallen in freefall under gravity:
h = 0.5 * g * t^2,
where h is the height of the building (12 m) and g is the acceleration due to gravity (approximately 9.81 m/s2). Rearranging for t gives us:
t = √(2 * h / g)
= √(2 * 12 / 9.81)
≈ 1.56 seconds.
Next, we calculate the horizontal distance traveled using the constant horizontal speed of the ball:
distance = speed * t
≈ 7.0 m/s * 1.56 s
≈ 10.92 m.
Therefore, the closest answer to the actual horizontal distance traveled is option a) 10.5 m.