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 750 m/s2 and the vertical or y component of its acceleration is 850 m/s2. The ball's mass is 0.39 kg. What is the magnitude of the net force acting on the soccer ball at this instant?

a = sqrt(750^2+850^2) = 1134 m/s^2.

F = m*a = 0.39 * 1134 = 442.1 N.

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.

Given:
Mass of the ball (m) = 0.39 kg
Horizontal acceleration (Ax) = 750 m/s^2
Vertical acceleration (Ay) = 850 m/s^2

Since the horizontal and vertical components of acceleration are perpendicular to each other, we can use the Pythagorean theorem to find the magnitude of the total acceleration (A) of the ball.

Using the Pythagorean theorem:
A² = Ax² + Ay²
A² = (750 m/s²)² + (850 m/s²)²
A² = 562500 m²/s⁴ + 722500 m²/s⁴
A² = 1287500 m²/s⁴

Taking the square root of both sides:
A = √(1287500 m²/s⁴)
A ≈ 1134.99 m/s² (rounded to 4 decimal places)

Now, we can calculate the magnitude of the net force (F) using Newton's second law:
F = m * A
F = (0.39 kg) * (1134.99 m/s²)
F ≈ 442.62 N (rounded to 2 decimal places)

Therefore, the magnitude of the net force acting on the soccer ball at this instant is approximately 442.62 Newtons.