Problem 110 - Fundamentals of Physics

Question

On average, an eye blink lasts about \(100 \mathrm{~ms}\). How far does a MiG-25 "Foxhat" fighter travel during a pilot's blink if the planc's average vclocity is \(3400 \mathrm{~km} / \mathrm{h} ?\)

Step-by-Step Solution

Answer

The MiG-25 travels approximately 94.52 meters during a pilot's blink.

Step 1: Convert Time from Milliseconds to Hours

First, we need to convert the blink time from milliseconds to hours because the velocity of the MiG-25 is given in kilometers per hour. We know that 1 second is equal to 1000 milliseconds, and 1 hour is 3600 seconds. Therefore, 100 milliseconds is converted to hours as follows: \[ 100 \text{ ms} = \frac{100}{1000} \text{ s} = 0.1 \text{ s} = \frac{0.1}{3600} \text{ hours} \approx 2.78 \times 10^{-5} \text{ hours} \].

Step 2: Calculate Distance Traveled During a Blink

The distance traveled can be calculated with the formula \( \text{distance} = \text{velocity} \times \text{time} \). Given the velocity \( v = 3400 \text{ km/h} \) and the time \( t \approx 2.78 \times 10^{-5} \text{ hours} \), we can find the distance using: \[ \text{distance} = 3400 \text{ km/h} \times 2.78 \times 10^{-5} \text{ hours} \approx 0.09452 \text{ km} \].

Step 3: Convert Kilometers to Meters

Since the answer asks for the distance during a blink, it might be more intuitive to express this in meters. To convert kilometers to meters, multiply by 1000: \[ 0.09452 \text{ km} \times 1000 \text{ m/km} = 94.52 \text{ meters} \].

Key Concepts

Understanding Unit Conversion

Converting units is crucial when solving physics problems. Different measurements can be in various units, so knowing how to convert between them is essential. In our example, we started with a blink time of 100 milliseconds and needed to convert it into hours. This is because the fighter plane's velocity is given in kilometers per hour.

Here's how we did it:

• Understand that 1 second (s) is equal to 1000 milliseconds (ms).
• Convert milliseconds to seconds by dividing by 1000.
• Recognize that 1 hour is equal to 3600 seconds.
• Convert seconds to hours by dividing the seconds by 3600.

For example, 100 ms becomes 0.1 s, which then is approximately 2.78 x 10^-5 hours. This type of conversion ensures our time units match our velocity unit.

Calculating Velocity and Its Role

Velocity tells us how fast something is moving and in what direction. It's important in physics because it combines speed and direction into a single vector quantity.

In our problem, the MiG-25 fighter plane had a velocity of 3400 km/h. To find out how far it travels during the blink of an eye, we used this velocity combined with the time we converted earlier. The key formula here is:

• Distance = Velocity x Time

By knowing the velocity, we can determine how much distance is covered over a specific duration. Multiplying the average velocity (3400 km/h) by our converted time (2.78 x 10^-5 hours) gave us the distance traveled during the blink.

Breaking Down Distance Calculation

Distance calculation is straightforward once you have the correct values for velocity and time. The formula to use is again:

• Distance = Velocity x Time

In our scenario, it was calculated that the distance covered by the MiG-25 during a blink (with an average velocity of 3400 km/h and time of 2.78 x 10^-5 hours) was approximately 0.09452 kilometers.

However, to be more tangible, we converted kilometers to meters by multiplying our result by 1000 (since 1 km = 1000 m). This final conversion yielded a distance of 94.52 meters, which is much easier to comprehend in the context of everyday distances.