21) The given situation states that two balls of different masses roll off a horizontal table with the same velocity. Looking at the answer choices, I can tell that they want us to compare the velocity and time the balls reach the ground, and the horizontal distance the balls travel.
We are going to kinematics to find this answer. We can set up an equation for both balls to find a relation for time.
Both balls start with the same velocity, drop the same distance, and are subject to the same acceleration of gravity. This means the equation for the large and small ball are the same; they will have the same solution for time.
Now we can take a look at the horizontal distplacement traveled. The only force acting on the balls is gravity. There are no forces in the x-direction, so there is no acceleration affecting the horizontal range.
Since both balls start with the same velocity, the x-components of the velocity will be the same. Also, as we proved above, the balls will have the same time in air. Thus, both of these equations are the same and will result in the same horizontal displacement.
We proved that both the large ball and the small ball will travel the same horizontal distance and hit the ground at the same time.
Answer: C
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