A soccer ball is kicked from ground level across a level soccer field with initial velocity vector v0 = 7 m/s at θ = 15° above horizontal. The soccer ball feels wind resistance which causes it to slow horizontally with constant acceleration magnitude ax = 0.66 m/s2, while leaving its vertical motion unchanged. Assume any other air resistance is negligible. Choose the positive direction of x from initial point towards final point of flight. Use a Cartesian coordinate system with the origin at the ball's initial position. A. Calculate the ball's time of flight, trin seconds.
B. Calculate the horizontal distance, Xmax in m, the ball travels before it returns to the soccer field.

A. t = 0.37 s

B. Xmax = 2.46 m.

Explanation:

A. The ball's time of flight can be found as follows:

Where:

t(f) is the time of flight

g is the gravity = 9.81 m/s²

is the initial speed in the vertical direction (y)                          

Hence the ball's time of flight is 0.37 s.

B. To find the maximum distance we need to use the next equation:

Where:

X₀ is the initial position = 0 (the origin in the Cartesian coordinate)

is the acceleration = 0.66 m/s²

Therefore, the horizontal distance the ball travels before it returns to the field is 2.46 m.

I hope it helps you!

54 degrees incident angle = reflected angle

angle is from normal turned to line of ray

3. dark matter

empty space could also be a simple vacuum