A projectile is fired vertically upwards from the ground. Does it take longer for the projectile to reach the apex of its trajectory or for the projectile to return from the apex back to the ground? Explain your reasoning. [Don't ignore air resistance]

(This is an A-level physics question of the type one might be expected to be asked during an oxbridge-style interview). Firstly, a free-body diagram of the forces acting on the projectile, as well as a velocity-time graph of the projectile's motion, could be drawn by the student to aid in their response to this question.To solve this problem the student must carefully consider and compare the direction of the forces (gravity and air resistance) acting on the projectile during the upwards journey (ground to apex) and the downwards journey (apex to ground).First note that the gravity force (i.e. the weight of the projectile) is constant and always acts vertically downwards (this is always true in projectile motion). We are left only to consider air resistance.Case 1 - Upwards trajectory: Since the projectile is travelling vertically upwards, and since air resistance always acts in the direction opposing velocity, it follows that the air resistance is acting vertically downwards, i.e. acting in the same direction as gravity.Case 2 - Downwards trajectory: Since the projectile is travelling vertically downwards, and since air resistance always acts in the direction opposing velocity, it follows that the air resistance is acting vertically upwards, i.e. opposing the force of gravity.The above reasoning has demonstrated an important fact: the average force acting on the projectile is larger on the upwards trajectory than on the downwards trajectory. A larger average force means a larger average acceleration (a = F/m), which, in this case, also means that the average speed of the projectile must be higher on the upwards trajectory than on the downwards trajectory (a velocity-time diagram helps to illustrate this fact) and, since the projectile travels the same distance in both the upward and downward trajectory, it must have taken longer for the projectile to travel this distance when its average speed was lower, i.e. on the downwards trajectory.