A ball with a horizontal speed of 0.33 m/s rolls off a bench 0.57 m above the floor. How far from a point on the floor directly below the edge of the bench will the ball land?

Answer 1

For anything moving freely in the air in both the horizontal and vertical direction, here are some things to remember:

1. Keep the horizontal math separate from the vertical math
2. The horizontal speed will not change (intro physics always ignores air friction)
3. The vertical motion will have an acceleration of "g" (9.81 m/s²) downwards.
4. The time in the air is the variable that's constant between horizontal and vertical motion. Typically, you will use the information given to find time in one direction, then switch over to the other direction and use that "t" value.

Here, the plan is to find "t" using the vertical information, then switch to horizontal and use v = d / t to find the horizontal distance

1. Vertical
2. When something falls off a table, it's the same as dropping it from your hand -- the initial vertical speed will be 0.
3. d = v_i * t + 1/2 * a * t²
4. Since we know d = 0.57m, v_i = 0 m/s, and a = 9.81 m/s² downwards, we can plug in and solve for "t" to find time.
5. Horizontal
6. Now we know "t", and we know that v_x = 0.33 m/s, so we can plug in to v = d / t to solve for the horizontal distance.