At an instant when a soccer ball is in contact with the foot of the player kicking it, the horizontal or x component of the ball's acceleration is 940 m/s2 and the vertical or y component of its acceleration is 710 m/s2. The ball's mass is 0.35 kg. What is the magnitude of the net force acting on the soccer ball at this instant?

To find the magnitude of the net force acting on the soccer ball, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration.

Formula:

Fnet = m * a

Where:
Fnet = Net force
m = Mass of the soccer ball
a = Acceleration of the soccer ball

Given:
m = 0.35 kg (mass of the soccer ball)
ax = 940 m/s^2 (horizontal/x component of acceleration)
ay = 710 m/s^2 (vertical/y component of acceleration)

To find the magnitude of the net force, we need to find the total acceleration of the soccer ball.

The total acceleration can be found using the Pythagorean theorem:

at = sqrt(ax^2 + ay^2)

Substituting the given values:

at = sqrt((940 m/s^2)^2 + (710 m/s^2)^2)

Calculating:

at = sqrt(882400 + 504100)

at = sqrt(1387500)

at ≈ 1177.35 m/s^2

Now, we can substitute the calculated total acceleration (at) and the given mass (m) into the equation for net force:

Fnet = m * at

Substituting the values:

Fnet = 0.35 kg * 1177.35 m/s^2

Calculating:

Fnet ≈ 411.06 N

Therefore, the magnitude of the net force acting on the soccer ball at this instant is approximately 411.06 N.