To find the speed at which the ball is thrown, we can use the equations of motion.
Firstly, let's consider the vertical motion of the ball. Since we know the height of the tower (h = 20 m), we can use the equation of motion for vertical displacement:
h = ut + (1/2)gt^2
where:
h = vertical displacement (20 m)
u = initial vertical velocity (0 m/s, since the ball is thrown horizontally)
g = acceleration due to gravity (9.8 m/s^2)
t = time of flight
We can rearrange this equation to solve for t:
20 = (1/2)(9.8)t^2
40 = 9.8t^2
t^2 = 40 / 9.8
t = √(40 / 9.8)
t ≈ 2.03 seconds
Now, let's consider the horizontal motion of the ball. The horizontal distance traveled by the ball (x = 56 m) can be found using the equation of motion for horizontal displacement:
x = ut
where:
x = horizontal displacement (56 m)
u = initial horizontal velocity
Since the ball is thrown horizontally, the initial horizontal velocity is the same as the final horizontal velocity. Therefore, we can rewrite this equation as:
x = vt
Now, we can solve for the horizontal velocity (v):
v = x / t
v = 56 m / 2.03 s
v ≈ 27.59 m/s
So, the ball is thrown at a speed of approximately 27.59 m/s.