- #1

Leo Liu

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- 156

- Homework Statement
- This is a statement

- Relevant Equations
- This is an equation

In the question above, the car's final velocity in the first case which is a group of people together jumping off the car, is less than that in the second case which is the same group of people jumping off the car one by one.

**My work (subquestion b only):**

$$M\Delta v=um \text{(from rocket equation)}$$

$$v_{i+t}-v_i=\frac{um}{M}$$

$$v_{j+1}=v_{j}+\frac{mu}{M_{j}}=v_j+\frac{um}{M+(N-j)m},$$

$$\text{j is the number of persons already jumped}$$

$$v_b=\sum_{j=0}^{N-1}\frac{um}{M+m(N-j)}$$

**My questions are as follows:**

1. For b, why is ##N-1## the upper bound of the series rather than ##N##?

2. Could you provide an intuition for why the final velocity of the car in b is greater than that in a although both cases expel the same amount of mass?

**Answer provided by my answer book:**

Thanks in advance!

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