A pool ball leaves a 0.75-meter high table with an initial horizontal velocity of 30 m/s. Predict the time required for the pool ball to fall to the ground.

time to fall:

h=1/2 g t^2
t=sqrt(2*.75/9.8)

distance=timeabove*30m/s

To calculate the time required for the pool ball to fall to the ground, we can use the equations of motion. The motion of the ball can be divided into two parts: horizontal motion and vertical motion.

Let's consider the vertical motion first. The ball falls under the influence of gravity. The key equation to use here is the one for vertical displacement:

d = v₀t + (1/2)gt²

Where:
- d is the vertical displacement (0.75 meters in this case)
- v₀ is the initial vertical velocity (0 m/s as the ball is not moving vertically initially)
- t is the time we want to calculate
- g is the acceleration due to gravity (approximately 9.8 m/s²)

Since the initial vertical velocity is zero, the equation simplifies to:

d = (1/2)gt²

Plugging in the values, we get:

0.75 = (1/2)(9.8)t²

Now we can solve for t²:

t² = (2 * 0.75) / 9.8
t² = 1.5 / 9.8

Finally, taking the square root of both sides to solve for t:

t = sqrt(1.5 / 9.8)

Calculating this value gives us the time required for the pool ball to fall to the ground, which is approximately 0.445 seconds.