To convert the value from meters per second to kilometers per hour, follow these steps:
1. Identify the given value:
We are given a speed of [tex]\(105\)[/tex] meters per second ([tex]\(\frac{m}{s}\)[/tex]).
2. Convert meters to kilometers:
One kilometer is equal to [tex]\(1,000\)[/tex] meters. Therefore, to convert meters to kilometers, you divide by [tex]\(1,000\)[/tex]:
[tex]\[
\frac{105 \, \text{meters}}{1} \times \frac{1 \, \text{kilometer}}{1,000 \, \text{meters}} = \frac{105}{1,000} \, \text{kilometers} = 0.105 \, \text{kilometers}
\][/tex]
3. Convert seconds to hours:
One hour is equal to [tex]\(3,600\)[/tex] seconds. Therefore, to convert seconds to hours, you multiply by [tex]\(3,600\)[/tex]:
[tex]\[
\frac{0.105 \, \text{kilometers}}{1 \, \text{second}} \times 3,600 \, \text{seconds per hour} = 0.105 \times 3,600 \, \text{kilometers per hour}
\][/tex]
4. Calculate the final value:
Multiply [tex]\(0.105\)[/tex] by [tex]\(3,600\)[/tex] to get the speed in kilometers per hour:
[tex]\[
0.105 \times 3,600 = 378.0 \, \text{kilometers per hour}
\][/tex]
Therefore, the value [tex]\(105 \, \frac{m}{s}\)[/tex] is equal to [tex]\(378.0 \, \frac{km}{h}\)[/tex].
[tex]\[
\boxed{378.0}
\][/tex]
