Question

Q58
Please help me as soon as possible.

Answer 1

Answer: 305.60 sec

Explanation:

Using the formula d=vt to solve. See image

Answer 2

305.6 seconds

Explanation:

To calculate how much longer it will take light to travel to Earth than to Mercury, we can use the formula for time:

`\large\boxed{\textsf{Time}\;(t) = \frac{\textsf{Distance}\;(d)}{\textsf{Speed}\;(s)}}`

Sun to Mercury

First, calculate the time it takes for light to travel from the Sun to Mercury.

Given:

• Distance: d = 5.792 × 10⁷ km
• Speed: s = 300,000 km/sec

Substitute the given values into the formula:

`\begin{aligned}\textsf{Time to Mercury}&=(5.792 * 10^7\;\sf km)/(300000\; \sf km/sec)\\\\&=(5.792 * 10^7\;\sf sec)/(300000)\\\\&=(57920000\;\sf sec)/(300000)\\\\&=(5792\;\sf sec)/(30)\\\\&=193.066666...\sf sec\end{aligned}`

Therefore, the approximate time it takes for light to travel from the sun to Mercury is 193.07 seconds (2 d.p.).

Sun to Earth

Now, calculate the time it takes for light to travel from the Sun to Earth:

Given:

• Distance: d = 1.496 × 10⁸ km
• Speed: s = 300,000 km/sec

Substitute the given values into the formula:

`\begin{aligned}\textsf{Time to Mercury}&=(1.496* 10^8\;\sf km)/(300000\; \sf km/sec)\\\\&=(1.496 * 10^8\;\sf sec)/(300000)\\\\&=(149600000\;\sf sec)/(300000)\\\\&=(1496\;\sf sec)/(3)\\\\&=498.666666...\sf sec\end{aligned}`

Therefore, the approximate time it takes for light to travel from the sun to Earth is 498.67 seconds (2 d.p.).

Difference

To find out how much longer it takes light to travel to Earth than to Mercury, subtract the time to Mercury from the time to Earth:

`\begin{aligned}\textsf{Time difference}&=\sf Time\;to\; Earth - Time\; to\; Mercury\\\\&=498.6666666... \;\textsf{seconds} - 193.066666... \;\textsf{seconds}\\\\&= 305.6\;\sf seconds\end{aligned}`

So, it will take approximately 305.6 seconds longer for light to travel from the Sun to Earth than to Mercury.

`\hrulefill`

Additional Information

As one calculation:

`\begin{aligned}\textsf{Time difference}&=\sf Time\;to\; Earth - Time\; to\; Mercury\\\\&=(1.496* 10^8\;\sf km)/(300000\; \sf km/sec)-(5.792 * 10^7\;\sf km)/(300000\; \sf km/sec)\\\\&=(1.496 * 10^8\;\sf sec)/(300000)-(5.792 * 10^7\;\sf sec)/(300000)\\\\&=(1.496 * 10^8\;\sf sec-5.792 * 10^7\;\sf sec)/(300000)\\\\&=(9.168 * 10^7)/(3 * 10^5)\;\sf sec\\\\&=3.056 * 10^2\; \sf sec\\\\&=305.6\; \sf sec\end{aligned}`