Question

A soccer ball is kicked with an initial speed of 12m/s at a 30-degree angle above the horizontal. Calculate the horizontal velocity and the initial vertical velocity. [Show all work, including the calculations with substitutions with units.]

Answer 1

x=10.39 m/s

y = 6 m/s

Step-by-step 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:

`x=r\cos\theta\\`

`y=r\sin\theta`

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:

`x=12~m/s\cos 30^\circ`

`x=12~m/s\cdot 0.866`

x = 10.39 m/s

`y=12~m/s\sin 30^\circ`

`y=12~m/s\cdot 0.5`

y = 6 m/s