Looking for reliable answers? Westonci.ca is the ultimate Q&A platform where experts share their knowledge on various topics. Connect with a community of experts ready to help you find accurate solutions to your questions quickly and efficiently. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.
Sagot :
Answer:
Approximately [tex]0.48\; \rm m\cdot s^{-1}[/tex].
Explanation:
Momentum would be conserved since there's no friction on this friend, and all other forces on her are balanced. Therefore:
[tex]\begin{aligned}& \text{Resultant momentum of (friend and pumpkin)} \\ =\; & \text{Initial momentum of (friend)} \\ & + \text{Initial momentum of (pumpkin)}\end{aligned}[/tex].
Momentum [tex]p[/tex] the product of mass [tex]m[/tex] and velocity [tex]v[/tex]. That is: [tex]p = m \, v[/tex].
The initial momentum of this friend is [tex]0\; \rm kg \cdot m \cdot s^{-1}[/tex] since she was initially not moving (an initial velocity of [tex]0\; \rm m\cdot s^{-1}[/tex].)
The initial momentum of the pumpkin would be:
[tex]\begin{aligned}p &= m \, v \\ &= 3.6 \; \rm kg \times 9.5\; \rm m\cdot s^{-1} \\ &= 34.2\; \rm kg \cdot m \cdot s^{-1}\end{aligned}[/tex].
Therefore:
[tex]\begin{aligned}& \text{Resultant momentum of (friend and pumpkin)} \\ =\; & \text{Initial momentum of (friend)} \\ & + \text{Initial momentum of (pumpkin)} \\ =\; &0\; {\rm kg \cdot m \cdot s^{-1}} + 34.2\; {\rm kg \cdot m \cdot s^{-1}} \\ =\; & 34.2\; {\rm kg \cdot m \cdot s^{-1}}\end{aligned}[/tex].
Rearrange the equation [tex]p = m \, v[/tex] to find an expression for velocity [tex]v[/tex] given momentum and mass:
[tex]\displaystyle v = \frac{p}{m}[/tex].
Note that the "final momentum of friend and pumpkin" in the previous equation refers to the resultant velocity of the friend with the pumpkin in her hand. Thus, it would necessary to use the combined mass of the friend and the pumpkin [tex](68\; {\rm kg} + 3.6 \; {\rm kg})[/tex] when calculating the resultant velocity:
[tex]\begin{aligned}& \text{Resultant velocity of (friend and pumpkin)} \\ =\; & \frac{\text{Resultant momentum of (friend and pumpkin)}}{\text{Mass of (friend and pumpkin)}} \\ =\; & \frac{34.2\; {\rm kg \cdot m \cdot s^{-1}}}{68\; {\rm kg} + 3.6\; {\rm kg}} \\ \approx \; & 0.48\; \rm m \cdot s^{-1}\end{aligned}[/tex].
We hope this was helpful. Please come back whenever you need more information or answers to your queries. We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Get the answers you need at Westonci.ca. Stay informed by returning for our latest expert advice.