The scenario that I'm having is such that a ball of radius $15mm$ is thrown from a location point $\vec{p}=(2, 5, 2)$ in a direction of $\vec{d}=(3, 0, 4)$. The initial velocity is $30m/s$. There were wind velocity at $15m/s$ in the direction of $\vec{v}=(0, 1, 0)$. The mass of the ball is $2kg$ and the gravity is $9.81m/s^2$.
I'm trying to calculate the time for the ball to hit the plane at $z=0$.
I started by making the throw direction as an unit vector: $\hat{\vec{d}} = \frac{\begin{bmatrix} 3\\ 0\\ 4 \end{bmatrix}}{\left | \begin{bmatrix} 3\\ 0\\ 4 \end{bmatrix} \right |}=\begin{bmatrix} \frac{3}{5}\\ 0\\ \frac{4}{5} \end{bmatrix}$
This is where the ball will reach at time $t$: $\vec{r(t)} = \vec{p}+t \cdot \hat{\vec{d}}$
$r_z = 2+t \cdot \frac{4}{5}$
Since equation of plane is $z=0$, if $z<15$, ball hits the plane:
$r_z < 15 \Rightarrow 2+t \cdot \frac{4}{5} < 15 \Rightarrow t\geq16.25$
This would imply that when $t\geq16.25$ seconds, the ball hits the plane. But I realise this doesn't consider the mass, gravity and wind resistance! So this value is probably invalid from start.
I recalled that $F=ma$, so $F= 2kg \cdot 9.81m/s^2$. But $F$ is just a scalar in this case and I don't know how I can use it any where.
How can I calculate the time $t$ for when the ball hits the plane with the consideration of the mass, gravity and wind resistance?