To find the time it takes for the ball to hit the ground, we can use the equation of motion for vertical motion:
h = v_i * t + (1/2) * a * t^2
Where: h is the vertical displacement (height) of the ball v_i is the initial vertical velocity (in this case, 0 m/s since the ball is thrown horizontally) a is the acceleration due to gravity (-9.8 m/s^2, assuming downward direction) t is the time
In this case, the initial vertical velocity is 0 m/s since the ball is thrown horizontally. The vertical displacement is 12 m (the height of the building), and the acceleration due to gravity is -9.8 m/s^2.
Plugging in these values into the equation, we get:
12 = 0 * t + (1/2) * (-9.8) * t^2
Simplifying the equation:
12 = -4.9 * t^2
Dividing both sides by -4.9:
t^2 = -12 / -4.9
t^2 = 2.4489
Taking the square root of both sides:
t ≈ 1.564 s
Therefore, it will take approximately 1.564 seconds for the ball to hit the ground.