# A 45kg boy is holding a 12kg pumpkin while standing on ice skates on a smooth frozen pond. The boy tosses the pumpkin with a horizontal speed of 2.8m/s to a 37kg girl (also wearing ice skates) catches it. What are the final speeds of the boy and girl?

Apr 6, 2018

Girl $| v | = 0.69 \frac{m}{s}$

Boy $| v | = 0.75 \frac{m}{s}$

#### Explanation:

For the boy holding the pumpkin, initial momentum is 0. After tossing it, he will have momentum equal and opposite that of the pumpkin:

$0 = 12 k g \cdot 2.8 \frac{m}{s} + 45 k g \cdot v$
$- 45 k g \cdot v = 33.6 k g \frac{m}{s}$
$v = - 0.747 \frac{m}{s}$
$| v | = 0.75 \frac{m}{s}$ <===the boy's final speed

For the girl, after catching the pumpkin she will have all the momentum the pumpkin had in flight:
$12 k g \cdot 2.8 \frac{m}{s} = \left(37 k g + 12 k g\right) \cdot v$
$- 33.6 k g \frac{m}{s} = 49 k g \cdot v$
$v = - 0.69 \frac{m}{s}$
$| v | = 0.69 \frac{m}{s}$<===the girl's final speed

Notice that both their momenta total to zero:
$45 k g \cdot 0.75 \frac{m}{s} = 49 k g \cdot 0.69 \frac{m}{s}$
$34 k g \frac{m}{s} = 34 k g \frac{m}{s}$

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