Momentum conservation in vertical direction. Confusion

Question

I was solving a problem from "An Introduction to Mechanics" by Kleppner and Kolenkow. The problem says..

A circus acrobat of mass $M$ leaps straight up with initial velocity $v_0$ from a trampoline. As he rises up, he takes a monkey of mass $m$ off a perch at height $h$ above trampoline. What is the maximum height attained by the pair?

Now I tried to solve the problem in many a way, but my answer didn't match. Ultimately, I used the conservation of momentum in the vertical direction and then the answer came out right. But previously I understood that momentum conservation cannot be applied in direction where there is a net external force acting on system. And here in this sum, gravity (an external force) is surely acting on the Acrobat-Monkey pair downwards. So can anyone tell me, how is the application of momentum in vertical direction justified in this problem, but not in problems involving projectile motion?

Duplicate - Can linear momentum be conserved before and after collision in the presence of an external force? — Farcher, Dec 06 '19 at 06:14
Does this answer your question? Can linear momentum be conserved before and after collision in the presence of an external force? — Mick, Dec 06 '19 at 08:15
Am I missing something here? Isn’t this a simple conservation of energy problem? — Bob D, Dec 06 '19 at 09:28
@BobD When the acrobat picks up the monkey, the acrobat undergoes an inelastic collision with the initially stationary monkey. This inelastic collision results in loss of energy, and thus the energy is not conserved. — , Dec 06 '19 at 12:17
@BobD The “collision” between the acrobat and the monkey is inelastic. — Farcher, Dec 06 '19 at 12:18
The "collision" is fairly long so the conservation of momentum is just an approximation. For many physics problems you can use approximations to obtain answers that can provide you useful information. For textbook problems, if you drill yourself enough you will know when such approximations are expected. — verdelite, Dec 06 '19 at 13:47

Momentum conservation in vertical direction. Confusion

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