Discover answers to your questions with Westonci.ca, the leading Q&A platform that connects you with knowledgeable experts. 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 :
To solve this problem, we need to apply the principle of conservation of momentum. Momentum is the product of mass and velocity, and for a closed system, the total momentum before an event must equal the total momentum after the event.
1. Step 1: Identify the masses and velocities.
- Mass of April: [tex]\( m_{April} = 55 \, \text{kg} \)[/tex]
- Mass of the watermelon: [tex]\( m_{watermelon} = 2 \, \text{kg} \)[/tex]
- Velocity of the watermelon before being caught: [tex]\( v_{watermelon} = 5 \, \text{m/s} \)[/tex]
- Initial velocity of April (and the skateboard) before catching the watermelon: [tex]\( v_{April,initial} = 0 \, \text{m/s} \)[/tex]
2. Step 2: Calculate the total initial momentum of the system.
Since April is initially at rest, her initial momentum is zero.
- Initial momentum of April: [tex]\( p_{April,initial} = m_{April} \times v_{April,initial} = 55 \times 0 = 0 \, \text{kg} \cdot \text{m/s} \)[/tex]
- Initial momentum of the watermelon: [tex]\( p_{watermelon} = m_{watermelon} \times v_{watermelon} = 2 \times 5 = 10 \, \text{kg} \cdot \text{m/s} \)[/tex]
Therefore, the total initial momentum of the system is:
[tex]\[ p_{total,initial} = p_{April,initial} + p_{watermelon} = 0 + 10 = 10 \, \text{kg} \cdot \text{m/s} \][/tex]
3. Step 3: Set up the conservation of momentum equation.
After catching the watermelon, April and the watermelon (plus the skateboard) will move together with a common final velocity [tex]\( v_{final} \)[/tex].
- The total mass after catching the watermelon: [tex]\( m_{total} = m_{April} + m_{watermelon} = 55 + 2 = 57 \, \text{kg} \)[/tex]
The total initial momentum must equal the total final momentum:
[tex]\[ p_{total,initial} = m_{total} \times v_{final} \][/tex]
4. Step 4: Solve for the final velocity [tex]\( v_{final} \)[/tex].
[tex]\[ 10 \, \text{kg} \cdot \text{m/s} = 57 \, \text{kg} \times v_{final} \][/tex]
Solving for [tex]\( v_{final} \)[/tex]:
[tex]\[ v_{final} = \frac{10}{57} \approx 0.175 \, \text{m/s} \][/tex]
5. Step 5: Compare the calculated final velocity with the provided choices.
- A. [tex]\( 5 \, \text{m/s} \)[/tex]
- B. [tex]\( 11 \, \text{m/s} \)[/tex]
- C. [tex]\( 0.18 \, \text{m/s} \)[/tex]
- D. [tex]\( 0.09 \, \text{m/s} \)[/tex]
The closest choice to [tex]\( 0.175 \, \text{m/s} \)[/tex] is C. [tex]\( 0.18 \, \text{m/s} \)[/tex].
Therefore, the correct answer is:
C. [tex]\(0.18 \, \text{m/s}\)[/tex]
1. Step 1: Identify the masses and velocities.
- Mass of April: [tex]\( m_{April} = 55 \, \text{kg} \)[/tex]
- Mass of the watermelon: [tex]\( m_{watermelon} = 2 \, \text{kg} \)[/tex]
- Velocity of the watermelon before being caught: [tex]\( v_{watermelon} = 5 \, \text{m/s} \)[/tex]
- Initial velocity of April (and the skateboard) before catching the watermelon: [tex]\( v_{April,initial} = 0 \, \text{m/s} \)[/tex]
2. Step 2: Calculate the total initial momentum of the system.
Since April is initially at rest, her initial momentum is zero.
- Initial momentum of April: [tex]\( p_{April,initial} = m_{April} \times v_{April,initial} = 55 \times 0 = 0 \, \text{kg} \cdot \text{m/s} \)[/tex]
- Initial momentum of the watermelon: [tex]\( p_{watermelon} = m_{watermelon} \times v_{watermelon} = 2 \times 5 = 10 \, \text{kg} \cdot \text{m/s} \)[/tex]
Therefore, the total initial momentum of the system is:
[tex]\[ p_{total,initial} = p_{April,initial} + p_{watermelon} = 0 + 10 = 10 \, \text{kg} \cdot \text{m/s} \][/tex]
3. Step 3: Set up the conservation of momentum equation.
After catching the watermelon, April and the watermelon (plus the skateboard) will move together with a common final velocity [tex]\( v_{final} \)[/tex].
- The total mass after catching the watermelon: [tex]\( m_{total} = m_{April} + m_{watermelon} = 55 + 2 = 57 \, \text{kg} \)[/tex]
The total initial momentum must equal the total final momentum:
[tex]\[ p_{total,initial} = m_{total} \times v_{final} \][/tex]
4. Step 4: Solve for the final velocity [tex]\( v_{final} \)[/tex].
[tex]\[ 10 \, \text{kg} \cdot \text{m/s} = 57 \, \text{kg} \times v_{final} \][/tex]
Solving for [tex]\( v_{final} \)[/tex]:
[tex]\[ v_{final} = \frac{10}{57} \approx 0.175 \, \text{m/s} \][/tex]
5. Step 5: Compare the calculated final velocity with the provided choices.
- A. [tex]\( 5 \, \text{m/s} \)[/tex]
- B. [tex]\( 11 \, \text{m/s} \)[/tex]
- C. [tex]\( 0.18 \, \text{m/s} \)[/tex]
- D. [tex]\( 0.09 \, \text{m/s} \)[/tex]
The closest choice to [tex]\( 0.175 \, \text{m/s} \)[/tex] is C. [tex]\( 0.18 \, \text{m/s} \)[/tex].
Therefore, the correct answer is:
C. [tex]\(0.18 \, \text{m/s}\)[/tex]
Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Get the answers you need at Westonci.ca. Stay informed by returning for our latest expert advice.
