To determine the resultant velocity of the airplane, we need to consider both the airplane's initial velocity and the tailwind velocity, as the tailwind aids the airplane's motion.
1. The airplane is traveling due east with an initial velocity of [tex]\( 7.5 \times 10^2 \)[/tex] kilometers/hour.
2. There is a tailwind with a velocity of 30 kilometers/hour, which will add to the airplane's initial velocity.
We calculate the resultant velocity by adding these two velocities:
[tex]\[ \text{Resultant Velocity} = 7.5 \times 10^2 \,\text{km/h} + 30 \,\text{km/h} \][/tex]
First, express [tex]\( 7.5 \times 10^2 \)[/tex] in a simpler form:
[tex]\[ 7.5 \times 10^2 = 750 \,\text{km/h} \][/tex]
Now, add the tailwind velocity to the initial velocity:
[tex]\[ 750 \,\text{km/h} + 30 \,\text{km/h} = 780 \,\text{km/h} \][/tex]
To match the format of the given answer choices (using scientific notation), we rewrite 780 kilometers/hour as:
[tex]\[ 780 \,\text{km/h} = 7.8 \times 10^2 \,\text{km/h} \][/tex]
Therefore, the correct answer is:
A. [tex]\( 7.8 \times 10^2 \)[/tex] kilometers/hour
