A graph of height versus time for an object thrown vertically upward is a parabola. The path of a projectile, thrown upward but not vertically upward, is also a parabola. Is this a coincidence? Justify your answer.

The height of the object thrown vertically upward with initial velocity v₀ can be calculated using Second Law of motion as:
One comparing the motion of object when thrown vertically upwards against the case when it was thrown in projectile, one can deduce that the vertical motion of the object in a projectile motion is similar to the object thrown vertically upwards except the fact that the magnitude of vertical speed of the object reduces significant.
It is not a mere coincidence that the height versus time graph for the object moving vertically upward is same as the object in projectile motion. the forces that acts on the object remain the same, therefore the trajectories of the object also follow the similar order.