Answer :
To solve this problem, we need to calculate Usain Bolt's average momentum during his 100-meter dash. Momentum is calculated using the formula:
[tex]\[ \text{Momentum} = \text{mass} \times \text{velocity} \][/tex]
Let's break down the steps to find the average momentum:
1. Calculate the Average Velocity:
- Velocity is defined as the distance traveled divided by the time taken.
- For Usain Bolt, the distance is [tex]\( 100 \)[/tex] meters, and the time taken is [tex]\( 9.58 \)[/tex] seconds.
- Therefore, the average velocity [tex]\( v \)[/tex] can be calculated as follows:
[tex]\[
v = \frac{\text{distance}}{\text{time}} = \frac{100 \, \text{meters}}{9.58 \, \text{seconds}} \approx 10.44 \, \text{m/s}
\][/tex]
2. Calculate the Momentum:
- Using the velocity we just calculated, and Bolt's mass of [tex]\( 94 \)[/tex] kg, we can find the momentum.
- The momentum [tex]\( p \)[/tex] is calculated by multiplying the mass by the velocity:
[tex]\[
p = \text{mass} \times \text{velocity} = 94 \, \text{kg} \times 10.44 \, \text{m/s} \approx 981.21 \, \text{kg m/s}
\][/tex]
Thus, Usain Bolt's average momentum during his 100-meter dash is approximately [tex]\( 981.21 \, \text{kg m/s} \)[/tex].
Based on the given options, the correct answer is:
[tex]\[ 981.21 \, \text{kg m/s} \][/tex]
[tex]\[ \text{Momentum} = \text{mass} \times \text{velocity} \][/tex]
Let's break down the steps to find the average momentum:
1. Calculate the Average Velocity:
- Velocity is defined as the distance traveled divided by the time taken.
- For Usain Bolt, the distance is [tex]\( 100 \)[/tex] meters, and the time taken is [tex]\( 9.58 \)[/tex] seconds.
- Therefore, the average velocity [tex]\( v \)[/tex] can be calculated as follows:
[tex]\[
v = \frac{\text{distance}}{\text{time}} = \frac{100 \, \text{meters}}{9.58 \, \text{seconds}} \approx 10.44 \, \text{m/s}
\][/tex]
2. Calculate the Momentum:
- Using the velocity we just calculated, and Bolt's mass of [tex]\( 94 \)[/tex] kg, we can find the momentum.
- The momentum [tex]\( p \)[/tex] is calculated by multiplying the mass by the velocity:
[tex]\[
p = \text{mass} \times \text{velocity} = 94 \, \text{kg} \times 10.44 \, \text{m/s} \approx 981.21 \, \text{kg m/s}
\][/tex]
Thus, Usain Bolt's average momentum during his 100-meter dash is approximately [tex]\( 981.21 \, \text{kg m/s} \)[/tex].
Based on the given options, the correct answer is:
[tex]\[ 981.21 \, \text{kg m/s} \][/tex]
