Answer:
x=10.39 m/s
y = 6 m/s
Explanation:
Components of a Vector
A vector can be expressed in several forms, including the rectangular and the polar form.
The rectangular form uses the x-y coordinates of the vector, being the right and up directions considered as positive.
The polar form uses the magnitude r and the angle it forms with the positive x-direction.
Given the polar form (r,θ), we can calculate the rectangular coordinates as follows:
[tex]x=r\cos\theta\\[/tex]
[tex]y=r\sin\theta[/tex]
The soccer ball is kicked with an initial speed of v=12 m/s and an angle of 30 degrees. Thus the horizontal and vertical components are:
[tex]x=12~m/s\cos 30^\circ[/tex]
[tex]x=12~m/s\cdot 0.866[/tex]
x = 10.39 m/s
[tex]y=12~m/s\sin 30^\circ[/tex]
[tex]y=12~m/s\cdot 0.5[/tex]
y = 6 m/s
