IDNLearn.com offers a comprehensive platform for finding and sharing knowledge. Ask your questions and receive reliable, detailed answers from our dedicated community of experts.
Sagot :
To determine the local speed of sound given the Mach number and the speed of the airplane, follow these steps:
1. Identify the given information:
- Mach number ([tex]\(M\)[/tex]) = 0.81
- Speed of the airplane ([tex]\(v_{airplane}\)[/tex]) = 850 km/h
2. Recall the relationship between Mach number, speed of the airplane, and the speed of sound:
- The Mach number is defined as the ratio of the speed of an object moving through a fluid to the local speed of sound.
- Mathematically, [tex]\( M = \frac{v_{airplane}}{v_{sound}} \)[/tex]
- Rearranging this formula to solve for the local speed of sound ([tex]\( v_{sound} \)[/tex]):
[tex]\[ v_{sound} = \frac{v_{airplane}}{M} \][/tex]
3. Substitute the given values into the formula:
[tex]\[ v_{sound} = \frac{850 \text{ km/h}}{0.81} \][/tex]
4. Perform the calculation:
- Divide 850 km/h by 0.81 to determine the local speed of sound.
- This results in:
[tex]\[ v_{sound} \approx 1049.3827160493827 \text{ km/h} \][/tex]
5. State the final answer:
- Therefore, the local speed of sound is approximately 1049.38 km/h.
Thus, the local speed of sound, given a Mach number of 0.81 and an airplane speed of 850 km/h, is approximately 1049.38 km/h.
1. Identify the given information:
- Mach number ([tex]\(M\)[/tex]) = 0.81
- Speed of the airplane ([tex]\(v_{airplane}\)[/tex]) = 850 km/h
2. Recall the relationship between Mach number, speed of the airplane, and the speed of sound:
- The Mach number is defined as the ratio of the speed of an object moving through a fluid to the local speed of sound.
- Mathematically, [tex]\( M = \frac{v_{airplane}}{v_{sound}} \)[/tex]
- Rearranging this formula to solve for the local speed of sound ([tex]\( v_{sound} \)[/tex]):
[tex]\[ v_{sound} = \frac{v_{airplane}}{M} \][/tex]
3. Substitute the given values into the formula:
[tex]\[ v_{sound} = \frac{850 \text{ km/h}}{0.81} \][/tex]
4. Perform the calculation:
- Divide 850 km/h by 0.81 to determine the local speed of sound.
- This results in:
[tex]\[ v_{sound} \approx 1049.3827160493827 \text{ km/h} \][/tex]
5. State the final answer:
- Therefore, the local speed of sound is approximately 1049.38 km/h.
Thus, the local speed of sound, given a Mach number of 0.81 and an airplane speed of 850 km/h, is approximately 1049.38 km/h.
Your participation means a lot to us. Keep sharing information and solutions. This community grows thanks to the amazing contributions from members like you. IDNLearn.com has the answers you need. Thank you for visiting, and we look forward to helping you again soon.