Three identical balls are thrown from the top of a building, all with the same initial speed. The first is thrown horizontally, the second at some angle above the horizontal, and the third at some angle below the horizontal. Neglecting air resistance, rank the speeds of the balls at the instant each hits the ground.
To answer this question, we need to analyze the motion of the balls.
Since we are neglecting air resistance, the only force acting on the balls is gravity, which causes them to accelerate downwards at a constant rate.
Let's analyze the horizontal motion of the balls first. The first ball is thrown horizontally, which means it has no initial vertical velocity. Therefore, it only experiences horizontal motion and its speed remains constant throughout its trajectory.
Now, let's consider the second ball thrown at an angle above the horizontal. This ball has both horizontal and vertical components of velocity. The vertical component contributes to the time it takes for the ball to reach the ground, but it does not affect the horizontal speed. When the ball hits the ground, its horizontal speed will be the same as the first ball because they both experienced the same horizontal acceleration (which is zero). Thus, the first and second balls will have the same horizontal speed at impact.
Lastly, let's analyze the third ball thrown at an angle below the horizontal. Similar to the second ball, its vertical component will impact the time it takes to reach the ground, but it will not affect the horizontal speed at impact. However, the horizontal component of velocity will be less than that of the first ball since it is thrown at an angle below the horizontal. Therefore, the third ball will have a lower horizontal speed at impact than the first two balls.
In summary, the ranking of the speeds of the balls at the instant each hits the ground is:
1. The first ball (thrown horizontally)
2. The second and third balls (thrown at an angle above and below the horizontal, respectively)
Please note that this analysis assumes no air resistance and equally inclined angles above and below the horizontal.