Draft
Main idea (simple step change)
Keep the given parametric motion for 0 ≤ t < t0.
At time t0 (when the wind strengthens) add a constant horizontal acceleration a_w for t ≥ t0 to model the stronger wind’s net horizontal push (a_w > 0 if the wind pushes the ball in the +x direction, a_w < 0 if it acts opposite).
Baseline (given) model
At time t0 (when the wind strengthens) add a constant horizontal acceleration a_w for t ≥ t0 to model the stronger wind’s net horizontal push (a_w > 0 if the wind pushes the ball in the +x direction, a_w < 0 if it acts opposite).
Baseline (given) model
From these the original constant accelerations are
Piecewise refined model (step increase at t0)
For t < t0 nothing changes:
For t < t0 nothing changes:
For t \ge t0 add the extra horizontal acceleration a_w (vertical motion unchanged in this simple model). Let
Then for t \ge t0