a soccer ball is kicked with an initial velocity of 5.0 m/s^2 in a direction of 30 degrees above the horizontal

a. what are the initial components of the velocity?
vix=
viy=
b. what are the components of the veloicty just before the ball hits the ground?
vx=
vy=

The inicial componente of velocity can be found by using SOH,CAH,TOA or it can be also be found by c^2= a^2 + b^2.

This is the way I did it.
To find y I used the sin of 50 in order to find one of the sides.
It would look something like this
sin(50)= y/25 (you may place a 1 on the bottom part of sin(50) so you could cross multiply)

After you cross multiply you should have -6.559=y ( that's your answer for the first part)

Now let's solve for the X component.
Since I find y and the problem already gives the hypotenuse, which is 25 m/s, you may now use the c^2= a^2 + b^2 formula. Or you may still used the SOH,CAH,TOA.
In this case I will use the first formula. It would be set up something like this:
(-6.559...)^2 + b^2 = (25)^2

43.025... + b^2= 625
( subtract the 43.025... From both sides)
b^2= 581.974
( now square up both sides so b can be by itself)
So your answer woulb be
b= 24.12

Sorry guys, both of my answers are wrong since I totally forgot to change my calculator into Degrees, you follow the same steps but now in Degrees.

The correct answers are
Y= 19.15 & X= 16.07
(Sorry for my mistake)

To solve this problem, we can break down the initial velocity vector into its horizontal and vertical components.

a. The initial velocity (5.0 m/s^2) can be broken down into its horizontal and vertical components using trigonometry. The horizontal component (vix) is determined by multiplying the initial velocity by the cosine of the angle. The vertical component (viy), on the other hand, is determined by multiplying the initial velocity by the sine of the angle.

vix = 5.0 m/s * cos(30 degrees)
viy = 5.0 m/s * sin(30 degrees)

Now we can calculate the values:

vix = 5.0 m/s * cos(30 degrees) ≈ 4.33 m/s
viy = 5.0 m/s * sin(30 degrees) ≈ 2.5 m/s

b. To find the components of the velocity just before the ball hits the ground, we need to consider that the only force acting on the ball is the vertical acceleration due to gravity. The horizontal component of the velocity (vx) remains constant throughout the motion, while the vertical component (vy) changes due to the acceleration.

vx = vix (horizontal component does not change)
vy = viy - g * t

Here, g is the acceleration due to gravity (approximately 9.8 m/s^2) and t is the time it takes for the ball to hit the ground.

Note that the time 't' can be calculated using kinematic equations, but for now, let's assume that the ball is kicked and hits the ground instantaneously (t = 0).

So, we can simplify the equations to:

vx = vix ≈ 4.33 m/s
vy = viy - g * t ≈ 2.5 m/s - 9.8 m/s^2 * 0 ≈ 2.5 m/s

Therefore, the components of the velocity just before the ball hits the ground are:

vx ≈ 4.33 m/s (horizontal component remains the same)
vy ≈ 2.5 m/s (vertical component remains the same)