Final answer:
The initial horizontal speed with which the ball was thrown was approximately 8.14 m/s, calculated by using the time taken by the ball to fall 24 m in a vertical free fall and the horizontal distance it traveled during that time.
Step-by-step explanation:
To determine with what speed the ball was thrown horizontally, we need to address the motion in two dimensions separately because the horizontal and vertical motions are independent. In the vertical direction, the ball is in free fall, so we can calculate the time it takes to hit the ground using the formula for the displacement in free fall: ½gt², where g is the acceleration due to gravity (approximately 9.81 m/s²) and t is the time.
Firstly, we determine the time of fall. As the vertical distance is 24 m, using the formula:
y = ½gt²
24 m = ½(9.81 m/s²)t²
From this equation, we can solve for t, and find that t is approximately 2.21 seconds. This is the time it takes for the ball to fall 24 m to the ground.
In the horizontal direction, the speed is constant as there is no acceleration (ignoring air resistance). Using this time of fall and knowing the horizontal distance of 18 m, we can now find the initial horizontal speed (v) with the formula:
s = vt
18 m = v(2.21 s)
Therefore, we can solve for v and find that the initial horizontal speed was approximately 8.14 m/s.