Determine velocity vector on sloped surface
A golf ball is launched at a speed v and launch angle, β . At some point the ball is located on the rim of a hole. The view from above looks as follows:
Vector v can be expressed in two components, vx and vy
$$ v_y = v \cdot \cos(\beta) $$
and
$$ v_x = v \cdot \sin(\beta) $$
If we look at the surface from a different angle, we see that the surface has a slope. 1002
The slope of the green is equal to φ (along the y-axis).
vv(ertical) is perpendicular to the y-axis. As a result:
$$ v_v = v \cdot \cos(\beta) \cdot \sin(\varphi) $$
Let's assume now there is no slope across the y-axis (φ=0), but there is a slope across the x-axis, θ.
Following the same logic vv is perpendicular to the x-axis. As a result:
$$ v_v = -1 \cdot v \cdot \sin(\beta) \cdot \sin(\theta) $$
What is the formula of vv expressed in terms of both φ and θ? So, in the case that the surface is sloped/inclined across both the x- and y-axis? 1002