1. **Problem Statement:** Find $r'(t)$, the velocity function of the rocket. 2. **Formula and Explanation:** Velocity is the first derivative of the position function $r(t)$ with respect to time $t$. That is, $$r'(t) = \frac{d}{dt} r(t)$$ 3. **Intermediate Work:** Since the exact function $r(t)$ is not provided in the prompt, the general step is to differentiate $r(t)$ term-by-term using derivative rules (power rule, constant multiple rule, sum rule). 4. **Plain Explanation:** To find the velocity, we take the derivative of the rocket's position function. This tells us how fast the rocket's position changes at any time $t$. 5. **Final Answer:** The velocity function is $r'(t) = \frac{d}{dt} r(t)$, which depends on the given $r(t)$. Note: Since the problem statement does not provide the explicit function $r(t)$, the velocity function $r'(t)$ cannot be explicitly calculated here. --- **Number of distinct questions found:** 5 (c)(i), (c)(ii), (d), (a) from Question 1, (b) from Question 1, etc., but only the first question (c)(i) is solved here as per instructions.