Video Transcript
Light from the Sun takes 13 minutes to reach one of the planets. Given that light travels at a speed of three multiplied by 10 to the power of eight meters per second, determine the distance between the Sun and that planet.
In this question, we need to work out the distance from the Sun to a planet when given the speed of light and the time it takes to travel that distance.
Recall that the formula for distance is given by distance is equal to speed multiplied by time. Before we can substitute the values for the speed and the time into this formula, we need to make sure that their units are compatible. We are told that the speed is three multiplied by 10 to the power of eight meters per second. Note that this number is written in scientific notation, which means it is of the form 𝑎 multiplied by 10 to the power of 𝑛, where the absolute value of 𝑎 must be greater than or equal to one and less than 10 and 𝑛 must be an integer.
Since the speed is in meters per second, it makes sense to convert the time of 13 minutes into seconds. To do this, we need to multiply 13 by the number of seconds in one minute, which is 60. Hence, the time taken for light to travel from the Sun to the planet is 780 seconds. Substituting into the distance formula, we have 780 multiplied by three multiplied by 10 to the power of eight, which simplifies to 2,340 multiplied by 10 to the power of eight. Since this isn’t in scientific notation, as our value of 𝑎 is not less than 10, we can rewrite 2,340 as 2.34 multiplied by 10 cubed. Next, we can use the product rule of exponents to simplify 10 cubed multiplied by 10 to the power of eight. This is equal to 10 to the power of 11, giving us a distance of 2.34 multiplied by 10 to the power of 11.
We can therefore conclude that the distance between the Sun and the planet is 2.34 multiplied by 10 to the power of 11 meters.
