Understanding the Problem: Calculating Airplane Distance

The question asks us to calculate the total distance covered by an airplane given its speed and the duration of its flight. The speed is provided in meters per second (m/s), and the time is given in hours. We need to find the distance in kilometers (km).

To solve this problem, we need to use the fundamental relationship between distance, speed, and time:

\(\text{Distance} = \text{Speed} \times \text{Time}\)

However, before we can directly apply this formula, we must ensure that the units are consistent. The speed is in m/s, and the time is in hours, but we need the final distance in km. Therefore, we need to convert the speed from m/s to km/h.

Converting Speed Units (m/s to km/h)

To convert speed from meters per second (m/s) to kilometers per hour (km/h), we need to consider the following conversion factors:

• 1 kilometer (km) = 1000 meters (m)
• 1 hour (h) = 60 minutes = 60 \(\times\) 60 seconds = 3600 seconds (s)

So, 1 m/s can be converted as follows:

\(1 \text{ m/s} = \frac{1 \text{ m}}{1 \text{ s}}\)

To convert meters to kilometers, we divide by 1000:

\(1 \text{ m} = \frac{1}{1000} \text{ km}\)

To convert seconds to hours, we divide by 3600:

\(1 \text{ s} = \frac{1}{3600} \text{ h}\)

Substituting these into the m/s expression:

\(1 \text{ m/s} = \frac{\frac{1}{1000} \text{ km}}{\frac{1}{3600} \text{ h}} = \frac{1}{1000} \times \frac{3600}{1} \text{ km/h} = \frac{3600}{1000} \text{ km/h} = 3.6 \text{ km/h}\)

So, the conversion factor from m/s to km/h is 3.6. We can multiply the speed in m/s by 3.6 to get the speed in km/h.

Given speed = 50 m/s.

\(\text{Speed in km/h} = 50 \text{ m/s} \times 3.6 \text{ km/h per m/s}\)

\(\text{Speed in km/h} = 180 \text{ km/h}\)

Calculating the Distance Covered

Now that we have the speed in km/h and the time in hours, we can calculate the distance in km.

• Speed = 180 km/h
• Time = 5 hours

Using the formula: \(\text{Distance} = \text{Speed} \times \text{Time}\)

\(\text{Distance} = 180 \text{ km/h} \times 5 \text{ hours}\)

\(\text{Distance} = 900 \text{ km}\)

Summary of Calculation Steps

The airplane will cover a distance of 900 km in 5 hours at a speed of 50 m/s.

Revision Table: Airplane Speed and Distance Calculation

Additional Information: Speed, Velocity, and Unit Conversion Tips

Speed vs. Velocity: In physics, speed is the magnitude of velocity. Speed is a scalar quantity (only magnitude), while velocity is a vector quantity (magnitude and direction). In this problem, we are only concerned with how fast the airplane is moving, so speed is the relevant concept.

Common Unit Conversions: It's helpful to remember common unit conversions for speed problems:

• m/s to km/h: Multiply by 3.6
• km/h to m/s: Divide by 3.6
• km to m: Multiply by 1000
• m to km: Divide by 1000
• hours to minutes: Multiply by 60
• minutes to seconds: Multiply by 60
• hours to seconds: Multiply by 3600

Mastering these conversions is key to solving many physics problems involving motion. Always check the units required for the final answer and ensure all given values are converted to compatible units before performing calculations.