“Instead of imagining the mass starting at rest at the apex of the dome, we will imagine it starting at the rim and that we give it some initial velocity directed exactly at the apex. If we give it too much initial velocity, it will pass right over the apex to the other side of the dome. So let us give it a smaller initial velocity. We produce the trajectory T1:”
As acceleration, jerk, snap, crackle, pop, … all must approach 0, does it ever actually reach the apex with zero velocity in finite time? That seems like the most obvious solution here where if you start with non zero velocity it never quite reaches the apex, and if you start with zero velocity at the apex it never leaves it.
As acceleration, jerk, snap, crackle, pop, … all must approach 0, does it ever actually reach the apex with zero velocity in finite time? That seems like the most obvious solution here where if you start with non zero velocity it never quite reaches the apex, and if you start with zero velocity at the apex it never leaves it.