Final answer:
To find the horizontal speed of a bowling ball rolled off a 2.00 m high table and landing 0.78 m away, we first calculate the time of free fall and then divide the horizontal distance by this time, yielding a speed of roughly 1.22 m/s.
Step-by-step explanation:
You wish to know how fast a bowling ball was rolling horizontally when it was rolled off a 2.00 m high table and landed on the ground 0.78 m from the base of the table. To solve this, we can use the principles of projectile motion from physics.
First, we should find the time the ball is in the air. We know the ball falls 2.00 m, so we use the equation for an object in free fall: d = (1/2)gt², where d is the distance, g is the acceleration due to gravity (9.8 m/s²), and t is the time. Rearranging the equation to solve for time, we get t = √(2d/g).
Plugging in the values, we have t = √(2 * 2.00 m / 9.8 m/s²). This calculates to approximately 0.64 seconds.
Knowing the time in the air, we can now determine the horizontal velocity (vx) of the ball using the equation vx = distance/time. Given that the ball lands 0.78 m from the table, we have vx = 0.78 m / 0.64 s, which equals approximately 1.22 m/s.
The bowling ball was rolling horizontally at about 1.22 m/s when it left the table.