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 930 m/s2 and the vertical or y component of its acceleration is 960 m/s2. The ball's mass is 0.34 kg. What is the magnitude of the net force acting on the soccer ball at this instant?

F = ma

what's the trouble? Forget your Pythagorean Theorem?

To find the magnitude of the net force acting on the soccer ball, we need to use Newton's second law of motion, which states that the net force acting on an object is equal to the product of its mass and acceleration:

Net Force = Mass × Acceleration

Given:
Mass of the soccer ball (m) = 0.34 kg
Horizontal component of acceleration (a_x) = 930 m/s^2
Vertical component of acceleration (a_y) = 960 m/s^2

First, we need to find the net acceleration acting on the soccer ball. The net acceleration can be found by combining the horizontal and vertical components using the Pythagorean theorem:

Net Acceleration (a_net) = √(a_x^2 + a_y^2)

Substituting the given values:
a_net = √(930^2 + 960^2) ≈ √(865,000) ≈ 930.6 m/s^2

Now, we can calculate the magnitude of the net force using Newton's second law:

Net Force = Mass × Net Acceleration
Net Force = 0.34 kg × 930.6 m/s^2 ≈ 316 N

Therefore, the magnitude of the net force acting on the soccer ball at that instant is approximately 316 Newtons.