### 1. Time for Light from the Sun to Reach Earth
The distance from the Sun to Earth is given as [tex]\(0.3 \times 10^7\)[/tex] miles. The speed of light is given as [tex]\(186 \times 10^3\)[/tex] miles per second.
To find the time it takes for light to travel from the Sun to Earth, we use the formula:
[tex]\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \][/tex]
First, calculate the time in seconds:
[tex]\[ \text{Time in seconds} = \frac{0.3 \times 10^7 \text{ miles}}{186 \times 10^3 \text{ miles/second}} \][/tex]
Performing the division:
[tex]\[ \text{Time in seconds} = \frac{3000000}{186000} \approx 16.129032258064516 \text{ seconds} \][/tex]
To convert the time from seconds to minutes, we divide by 60:
[tex]\[ \text{Time in minutes} = \frac{16.129032258064516 \text{ seconds}}{60} \approx 0.26881720430107525 \text{ minutes} \][/tex]
So, it takes approximately 16.129 seconds or 0.269 minutes for light to travel from the Sun to Earth.
### 2. Difference in Distance Between Jupiter and Mars
The distance from the Sun to Jupiter is [tex]\(4.84 \times 10^7\)[/tex] miles, and the distance from the Sun to Mars is [tex]\(1.42 \times 10^7\)[/tex] miles.
To find the difference in their distances, we subtract the distance to Mars from the distance to Jupiter:
[tex]\[ \text{Difference} = (4.84 \times 10^7) - (1.42 \times 10^7) \][/tex]
Calculate the difference in distance:
[tex]\[ \text{Difference} = 4.84 \times 10^7 - 1.42 \times 10^7 \][/tex]
[tex]\[ \text{Difference} = (4.84 - 1.42) \times 10^7 \][/tex]
[tex]\[ \text{Difference} = 3.42 \times 10^7 \text{ miles} \][/tex]
So, the difference in distance between Jupiter and Mars is 34,200,000 miles or 3.42 × 10^7 miles expressed in scientific notation.
### 3. Distance Light Travels in 0.5 Minutes
Light travels at a speed of [tex]\(186 \times 10^3\)[/tex] miles per second. We need to calculate the distance light travels in [tex]\(\frac{1}{2}\)[/tex] minute, or 30 seconds.
First, convert 0.5 minutes to seconds:
[tex]\[ 0.5 \text{ minutes} \times 60 \text{ seconds/minute} = 30 \text{ seconds} \][/tex]
To find the distance light travels in 30 seconds, use the formula:
[tex]\[ \text{Distance} = \text{Speed} \times \text{Time} \][/tex]
Substituting the values:
[tex]\[ \text{Distance} = 186 \times 10^3 \text{ miles/second} \times 30 \text{ seconds} \][/tex]
Calculate the distance:
[tex]\[ \text{Distance} = 186000 \times 30 = 5580000 \text{ miles} \][/tex]
So, light will travel 5,580,000 miles in [tex]\(\frac{1}{2}\)[/tex] minute.
