From a collision to a pendulum rise

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Problem: From a collision to a pendulum rise
A 0.010 kg projectile moving horizontally at 100 m/s embeds in a stationary 0.990 kg pendulum block. The combined mass then rises freely.
Question: Find the maximum vertical rise after impact.
Givens:
- m = 0.010 kg
- M = 0.990 kg
- u = 100 m/s
Assumptions: g = 10 m/s²; negligible horizontal external impulse during impact; projectile sticks; no dissipative loss during the subsequent swing.
Choices (LaTeX):
A. 0.10\ \mathrm m
B. 500\ \mathrm m
C. 0.050\ \mathrm m
D. 5\ \mathrm m

Ask for my approach first. Help me distinguish a physical misconception from an algebra error without revealing which choice is correct.

Tutoring approach:
Act as a patient physics tutor. Ask what I understand and what I have tried, then wait for my reply. Teach one step at a time; do not give the final answer or a complete solution immediately. Start with a physical picture. Define unfamiliar symbols and operators, explain signs and units, and state the model's assumptions. Give progressively stronger hints only when I need them. Ask me to predict a change before calculating it. When I finish, help me check dimensions and a limiting case, then ask one related transfer question. If information is missing or ambiguous, ask rather than inventing it. Distinguish exact results from approximations and acknowledge uncertainty.