A ball is thrown horizontally from the roof of a building 60 m tall and lands 45 m from the base. What was the ball's initial speed?

_______m/s

How long does it take to fall 60M?

what is that time divided into 45m?

To find the ball's initial speed, we can use the kinematic equation that relates the horizontal distance traveled, the initial velocity, and the time of flight.

The vertical motion of the ball can be disregarded because it is thrown horizontally. So, the only force acting on the ball is gravity in the vertical direction.

Considering the vertical motion:
- Initial position (y₀) = 60 m
- Final position (y) = 0 m
- Initial velocity in the vertical direction (v₀y) = 0 m/s (since the ball is thrown horizontally)
- Acceleration due to gravity (g) = 9.8 m/s²

We can use the vertical motion equation to find the time of flight (t):

y - y₀ = v₀y * t + (1/2) * g * t²

Plugging in the values:
0 - 60 = 0 * t + (1/2) * 9.8 * t²
-60 = (1/2) * 9.8 * t²
-120 = 9.8 * t²
t² = -120 / 9.8
t² ≈ -12.24

Since time cannot be negative, we discard the negative solution. Therefore, t² ≈ 12.24.

Now that we have the time of flight, we can use the horizontal motion equation to find the initial velocity (v₀x):

x = v₀x * t

Plugging in the values:
45 = v₀x * t
45 = v₀x * √12.24 (taking the square root of t²)

Solving for v₀x, we have:
v₀x = 45 / √12.24
v₀x ≈ 12.97 m/s

Therefore, the ball's initial speed (v₀) is approximately 12.97 m/s (rounded to two decimal places).