At an instant when a soccer ball is in contact with the foot of a player kicking it, the horizontal or x component of the ball's acceleration is 860 m/s2 and the vertical or y component of its acceleration is 1030 m/s2. The ball's mass is 0.38 kg. What is the magnitude of the net force acting on the soccer ball at this instant?

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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 force acting on an object is equal to the mass of the object multiplied by its acceleration.

Given:
- Mass of the soccer ball (m) = 0.38 kg
- Horizontal component of acceleration (ax) = 860 m/s^2
- Vertical component of acceleration (ay) = 1030 m/s^2

We can use these values to calculate the net acceleration (a) of the soccer ball using the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides.

Using the Pythagorean theorem:
a = √(ax^2 + ay^2)

Substituting the given values:
a = √((860 m/s^2)^2 + (1030 m/s^2)^2)
= √(739,600 m^2/s^4 + 1,060,900 m^2/s^4)
= √(1,800,500 m^2/s^4)
≈ 1,342 m/s^2

Now, we can calculate the magnitude of the net force (F) acting on the soccer ball using Newton's second law:
F = m * a

Substituting the given mass and calculated acceleration:
F = 0.38 kg * 1,342 m/s^2
≈ 509.96 N

Therefore, the magnitude of the net force acting on the soccer ball at this instant is approximately 509.96 Newtons.