A meteoroid is speeding through the atmosphere, traveling east at 23.1 km/s while descending at 11.9 km/s. What is its speed, in km/s?
down is perpendicular to east (Google "orthogonal")
That means that the resultant is the hypotenuse of the triangle with legs of 23.1 east and 11.9 down.
resultant speed = sqrt(23.1^2 + 11.9^2)
for example:
https://www.physicsclassroom.com/class/vectors/Lesson-1/Component-Addition
or
https://en.wikipedia.org/wiki/Orthogonality
To find the meteoroid's speed, we can use the Pythagorean theorem. The theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the meteoroid's speed in the east direction and the speed in the descending direction form the two sides of a right triangle. Let's call the eastward speed "v_e" and the descending speed "v_d".
According to the given information, v_e = 23.1 km/s and v_d = 11.9 km/s.
To find the overall speed (the hypotenuse), we can use the Pythagorean theorem as follows:
speed^2 = v_e^2 + v_d^2
speed^2 = (23.1 km/s)^2 + (11.9 km/s)^2
speed^2 = 533.61 km^2/s^2 + 141.61 km^2/s^2
speed^2 = 675.22 km^2/s^2
To find the speed, we take the square root of both sides:
speed = √(675.22 km^2/s^2)
speed ≈ 26 km/s
Therefore, the meteoroid's speed is approximately 26 km/s.