A person initially at rest throws a ball upward at an angle θ0 with an initial speed v0. He tries
to catch up to the ball by accelerating with a constant acceleration a for a time interval ∆t1
and then continues to run at a constant speed for a time interval ∆t2. He catches the ball at
exactly the same height he threw the ball. Let g be the gravitational constant. What was the
person’s acceleration a ?