A soccer ball travelling at 15 m/s [E] bounces off of a goal post and ends up moving 12 m/s [S 30¡Æ E]. If the ball was in contact with the post for 0.10 seconds, calculate the acceleration of the ball.

To calculate the acceleration of the ball, we need to use the equation of motion:

Acceleration = (Change in velocity) / Time

First, we need to determine the change in velocity of the ball. The initial velocity is 15 m/s [E], and the final velocity is 12 m/s [S 30¡Æ E]. Since the final velocity is given as a vector in the direction of South 30¡Æ East, we need to resolve it into its components in the horizontal (east-west) and vertical (north-south) directions.

To do this, we can use trigonometry. The angle given is 30 degrees, and the hypotenuse is the magnitude of velocity, which is 12 m/s. We can use the following trigonometric equations to find the east-west and north-south components:

Vertical Component = 12 × sin(30¡Æ)
Horizontal Component = 12 × cos(30¡Æ)

Once we have the components, we can calculate the change in velocity:

Change in east-west velocity = (Final east-west velocity) - (Initial east-west velocity)
Change in north-south velocity = (Final north-south velocity) - (Initial north-south velocity)

Finally, we can calculate the acceleration using the formula mentioned earlier:

Acceleration = (Change in velocity) / Time

So, let's plug in the values and calculate the acceleration:

Vertical Component = 12 × sin(30¡Æ) ≈ 6 m/s
Horizontal Component = 12 × cos(30¡Æ) ≈ 10.39 m/s

Change in east-west velocity = 10.39 m/s - 15 m/s = -4.61 m/s
Change in north-south velocity = 6 m/s - 0 m/s = 6 m/s

Acceleration = (Change in velocity) / Time
Acceleration = (sqrt((Change in east-west velocity)^2 + (Change in north-south velocity)^2)) / Time

However, the time of contact (0.10 seconds) is not sufficient to calculate the acceleration accurately. To get a more precise value, we need more information, such as the mass of the ball or the force of impact.