A football is kicked with a velocity of 31 m/s at an angle of 41. What is the ball's acceleration in the vertical direction as it flies through the air?

-g = -9.8 m/s^2

The angle and the speed don't matter.
Gravity provides the acceleration

g, 9.81 m/s^2 downward

To determine the ball's acceleration in the vertical direction, we first need to split the initial velocity into its horizontal and vertical components.

Given:
Initial velocity (v) = 31 m/s
Launch angle (θ) = 41°

Vertical Component (v_y):
v_y = v * sin(θ)

Horizontal Component (v_x):
v_x = v * cos(θ)

Now, let's calculate the vertical component of velocity first:
v_y = v * sin(θ)
v_y = 31 m/s * sin(41°)
v_y ≈ 31 m/s * 0.6561
v_y ≈ 20.3141 m/s

Since we know that the acceleration due to gravity acts in the vertical direction, we can say that the ball's acceleration in the vertical direction is equal to the acceleration due to gravity (g) which is approximately 9.8 m/s². This is because there are no other significant vertical forces acting on the ball while it flies through the air.

Therefore, the ball's acceleration in the vertical direction is approximately 9.8 m/s².