Question

Find the vertical and horizontal component?

Answer 1

`V_h" is "30 m/s and V_v" is "7.5 m/s`

Explanation:

That line `76^@` from the vector does not look vertical in the figure, but I will assume it is meant to be. I am going to put m/s with the value 31 because the magnitude of a vector should have units.

I have inserted a figure. The 31 m/s vector is shown in black and the 2 components are shown in blue.

The vector is the hypotenuse of the triangle formed by the 2 components and the 31 m/s resultant of the 2 components. Since the hypotenuse will be involved in the calculations, the trigonometry functions we need to be interested in are sine and cosine.

`sin76^@ = "opposite"/"hypotenuse"`
`cos76^@ = "adjacent"/"hypotenuse"`
The opposite side is the horizontal component and the adjacent side is the vertical component. Therefore,

`V_h = 31 (m/s)*sin76^@ = 30 m/s`

`V_v = 31 (m/s)*cos76^@ = 7.5 m/s`

You will come to realize that the trig function that would work for many similar questions will be either sine or cosine. My way to find which is the right function for the occasion is to ask "if the angle were zero (or sometimes 90), which function would give the proper result".

If you asked yourself that question on this problem, it would be better in this case to suppose the angle were `90^@`. If the angle were to increase to 90, the 31 m/s would be completely horizontal, so there would be no vertical component. Between sine and cosine, which would say that the vertical component is zero? `Cos90^@` is zero, so use cos76 for the vertical and sin76 for the horizontal.

I hope this helps,
Steve