A pool ball flies horizontally off of a table that is 1 meter high and flies 1 meter away from the table before hitting the ground. What is the initial velocity and the final velocity when it hits?
To determine the initial velocity and final velocity of the pool ball, we can use the principles of projectile motion.
First, we need to consider the vertical motion of the ball. We know that the ball was initially at a height of 1 meter and fell vertically down to the ground. We can use the equation for vertical displacement during free fall:
d = (1/2) * g * t^2
Where:
- d is the vertical displacement (1 meter in this case)
- g is the acceleration due to gravity (approximately 9.8 m/s^2)
- t is the time it takes for the ball to fall
Since the ball falls vertically, the horizontal motion does not affect the vertical displacement. Therefore, we can ignore the horizontal motion for now.
Rearranging the equation, we get:
t^2 = (2 * d) / g
Substituting the given values, we have:
t^2 = (2 * 1) / 9.8
t^2 ≈ 0.204
Taking the square root of both sides of the equation, we find:
t ≈ 0.452 seconds
Now, we can use the horizontal motion to find the initial velocity, assuming no air resistance. The horizontal distance traveled by the ball is 1 meter, and the time it takes for the ball to reach that distance is 0.452 seconds.
The formula for horizontal distance is:
d = v * t
Where:
- d is the horizontal distance (1 meter in this case)
- v is the horizontal component of the velocity
- t is the time taken to reach the distance
Rearranging the equation, we can solve for v:
v = d / t
Substituting the given values, we have:
v = 1 / 0.452
v ≈ 2.21 m/s
Therefore, the initial velocity of the pool ball is approximately 2.21 m/s.
Finally, let's consider the final velocity when the ball hits the ground. Since the motion is vertical, and there is no air resistance, the final vertical velocity is the same magnitude as the initial vertical velocity, but in the opposite direction. Therefore, the final vertical velocity is approximately -9.8 m/s.
However, the final horizontal velocity remains the same as the initial horizontal velocity, which is approximately 2.21 m/s.
In conclusion, the initial velocity of the pool ball is approximately 2.21 m/s, and the final velocity when it hits the ground is approximately 2.21 m/s horizontally and -9.8 m/s vertically.