Final answer:
The ball hits the floor approximately 5.50 meters horizontally from point A.
Step-by-step explanation:
To find the horizontal distance the ball travels before hitting the floor, we can use the principle of conservation of energy. The initial potential energy of the ball at height H is equal to the sum of its final potential energy at height h and its final kinetic energy at the moment of impact.
Using the formula for potential energy (PE = mgh) and kinetic energy (KE = 0.5mv^2), we can set up the equation:
mgh = mgh + 0.5mv^2
Simplifying and solving for v, we get:
v = sqrt(2g(h - h))
Substituting the given values, we have:
v = sqrt(2 * 9.8 * (5.9 - 1.9)) = sqrt(78.4) = 8.85 m/s
Now, we can use the formula for horizontal distance (d = vt) to find the distance the ball travels:
d = 8.85 m/s * t
where t is the time it takes for the ball to hit the floor.
Since the ball starts from rest, we can use the equation:
h = 0.5gt^2
Substituting the given values, we have:
1.9 m = 0.5 * 9.8 * t^2
Solving for t, we get:
t = sqrt(1.9 / (0.5 * 9.8)) = sqrt(0.3878) = 0.622 s
Finally, substituting the value of t into the formula for horizontal distance, we get:
d = 8.85 m/s * 0.622 s = 5.50 m