Question wording- incline question

[caljuice]

The question was:

A 4.5-kg mass is given an initial velocity of 14 m/s up an incline that makes an angle of 37o with the horizontal. When its displacement is 8.0 m, its upward velocity has diminished to 5.2 m/s.

I'm confused with directions of the velocity. In the solution they used the equation

vf²=vi²+2*a*d

anyway to find 'a' they subtracted (14²-5.2²)/(2*8)

So doesn't this mean initial velocity and the upward velocity are parallel since they are being subtracted. I assumed the initial velocity would be parallel to the incline and the upward velocity completely vertical and thus i would have to 5.2/sin37.

When you read the question, what direction would you assume? Maybe it's right and I'm just mixing up the axis?

 

[HallsofIvy]

Why would you assume the upward velocity was "completely vertical"? If the object were moving vertically, there would be no reason to mention the incline! The object is moving up the inclined plane. Yes, its velocity is always parallel to the incline.

 

[kerimek]

Based on the given information and the equation used in the solution, it appears that the initial velocity and the upward velocity are indeed parallel. This is because the equation used, vf^2 = vi^2 + 2ad, is a scalar equation and does not take into account the direction of the velocities. Therefore, the direction of the initial velocity and the upward velocity does not affect the calculation of acceleration.

However, if you were to consider the direction of the velocities, it is important to note that the initial velocity is parallel to the incline while the upward velocity is not completely vertical. This is because the incline makes an angle of 37o with the horizontal, so the upward velocity will have a component in the horizontal direction as well.

To avoid confusion, it is important to clearly define the direction of the velocities in the problem statement. In this case, it would be helpful to specify that the initial velocity is parallel to the incline and the upward velocity is in the vertical direction. This will help to ensure that the correct equations and calculations are used.

In summary, while the solution to the problem may be correct, it would be helpful to clarify the directions of the velocities in the problem statement to avoid any confusion.