Question

Given that average speed is distance traveled divided by time, determine the values of m and n when the time it takes a beam of light to get from the sun to the earth (in s) is written in scientific notation. note: the speed of light is approximately 3.0×108m/s.

Answer 1

The distance  of earth from sun is 150 million km

We know that one million = 10^6 and 1 km= 10^3 m

Hence 150 million km = 150× 10^6 ×10^3 metre=150×10^9 m

                                                                                  =1.5×10^11 m

The speed of light in vacuum is  2.999... m/s which can be approximately close to  3.0 ×10^8 m/s

We are asked to calculate the time taken by the light beam to reach from sun to earth.

we know that average velocity $v=\frac{distance}{time}$

                                                       ⇒ $time= \frac{distance}{velocity}$

Here distance=1.5×10^11 m and v=c= 3.0×10^8 m/s

                            hence time $[t]=\frac{1.5*10^{11} }{3.0*10^{8} } second$

                                                           =0.5×10^3 s

                                                            =5.0×10^2 s

 A correct scientific notation  is written as m×10^n   [Here m is the magnitude and n is power of 10]                                                      

Hence the value of m =5 and value of n =2

Answer 2

The value of $m$ is $\boxed{5}$ and the value of $n$ is $\boxed{2}$.

Further Explanation:

Given:

The distance of the sun from the Earth is about $150\;\text{million km}$.

The speed of the light coming from the sun is $3\times10^{8}\;\text{m/s}$.

The time taken by the sunlight to reach the Earth is $m\times10^{n}\;\text{s}$.

Concept:

The time taken by the sunlight from the sun to reach the Earth is expressed as the ratio of the distance and the speed at which the light travels from the sun to reach the Earth.

The time taken by the sunlight can be expressed as.

 $\boxed{\text{time}=\frac{\text{distance}}{\text{speed}}}$

Convert the distance of the sun from Earth into scientific notation.

$\begin{aligned}150\;\text{millionkm}&=150\times10^{6}\text{km}\\&=150\times10^{6}\times10^{3}\text{m}\\&=1.5\times10^{11}\text{m}\end{aligned}$

Substitute the values of distance and speed in above expression.

 $\begin{aligned}\text{time}&=\frac{1.5\times10^{11}}{3\times10^{8}}\text{s}\\&=0.5\times10^{3}\text{s}\\&=5\times10^{2}\text{s}\end{aligned}$

Comparing the time taken by the light to the value in terms of $m$ and $n$.

 $m\times10^n=5\times10^2\;\text{s}$

Therefore, from the above expression, the value of $m$ is $\boxed{5}$ and the value of $n$ is $\boxed{2}$.

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Answer Details:

Grade: High School

Chapter: Scientific Notations

Subject: Physics

Keywords: Light, speed, distance, 150 million kilometer, values of m and n, light to get, sun to the earth, scientific notation, speed of light.