Two objects are thrown vertically upward, first one, and then, a bit later, the other. is it (a) possible or (b) impossible that both objects reach the same maximum height at the same instant of time?

No, it is impossible

Explanation:

Kinematics equation:

if height is maximum:

y=H and Vf=0

so:

Analysis: From the last equation we see that the maximum height depends ONLY on the initial speed. This means that if both objects reach the same maximum height, then they necessarily need to have the SAME initial velocity. If they have the same initial velocity and in order to reach the maximum height at the SAME time the only way is that they are released at the SAME TIME.

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