Final velocity vs. horizontal velocity for a car rolling off a desk

[JWest]

Which way is closer to the actually velocity of a car rolling down a ramp and falling off a desk to the floor? Finding the final velocity (Vf) or finding the horizontal velocity (Vx)? Why?

 

[ceptimus]

You really need to calculate the horizontal velocity component Vx, and the vertical velocity component Vy, then you can combine the two together to get the final velocity you call Vf. You can draw a right angled triangle with Vx and Vy as the two shorter sides, and Vf will be the length of the hypotenuse.

Now I don't have the diagram, so I'm not sure how the ramp is placed on the desk. Is the ramp right on the edge of the table, so the car is still going down it before it falls, or is there a length of flat table after the ramp, before the car falls off?

If there is some flat horizontal table between the ramp and the edge, then you know that the car's initial downward velocity Vy is zero, and its final downward velocity will just be due to the fall from the height of the table. If the car is still going down the ramp, you need to figure how fast it's going across and down, as it comes off the end.

Either way, once the car is clear of the table, its horizontal velocity Vx won't change, and only Vy will increase due to the force of gravity.

 

[wais]

The more accurate measure of the velocity of a car rolling down a ramp and falling off a desk to the floor would be finding the final velocity (Vf) rather than the horizontal velocity (Vx). This is because the final velocity takes into account both the horizontal and vertical components of the car's motion, while the horizontal velocity only considers the horizontal component.

When a car rolls off a desk, it is not only moving horizontally but also vertically as it falls to the floor. Therefore, the final velocity, which considers both of these components, would give a more accurate representation of the car's overall velocity. On the other hand, the horizontal velocity only considers the car's motion in the horizontal direction and does not take into account its vertical motion, making it a less accurate measure of the car's velocity.

Additionally, finding the final velocity would also consider the effects of air resistance and friction, which would impact the car's overall velocity as it rolls down the ramp and falls off the desk. These factors would not be accounted for when finding the horizontal velocity, making it even less accurate.

In conclusion, the final velocity (Vf) would be a more accurate measure of the car's velocity in this scenario as it takes into account both the horizontal and vertical components of its motion, as well as other external factors that may affect its velocity.