Question

Light from the sun takes about $ 8.0 $ min to reach earth. How far away is the Sun?

Answer 1

Hint :We know that the light from the sun takes $ 8.0 $ min to reach the earth and we have to calculate the distance between the sun and the earth. To calculate the distance we have to use the formula of the velocity where we have to use the speed of light in vacuum and the velocity is the rate of change of distance with respect to time.

Complete Step By Step Answer:
Let us use the formula of velocity and velocity is the rate of change of distance with respect to time. From this we can find the distance from Sun to earth and time taken by the light is $ 8.0 $ min.
 $ \Rightarrow v = \dfrac{d}{t} $ … $ (1) $
Where,
 $ v $ - Velocity of light in vacuum.
 $ d $ - Distance between sun and earth.
 $ t $ - Time taken by light from sun to reach the earth.
Now, put the value of $ v $ as $ 3 \times {10^8}m{s^{ - 1}} $ in vacuum in equation $ (1) $ .
Thus, equation $ (1) $ is given by:
 $ \Rightarrow 3 \times {10^8}m{s^{ - 1}} = \dfrac{d}{{8 \times 60\operatorname{s} }} $ … (Since, velocity is in $ m{s^{ - 1}} $ and time is to be taken as in seconds too)
 $ \Rightarrow d = 3 \times {10^8} \times 8 \times 60m $
 $ \Rightarrow d = 144 \times {10^9}m $
Thus, the answer is obtained as $ 144 \times {10^9}m $ and $ 144\;000\;000kilometers $ .

Note :
Thus, we found out that the distance between sun and earth from the formula of velocity at the rate of change of distance with respect to time. So, we found out the distance travelled by the light from sun to earth.