A meteoroid is speeding through the atmosphere, traveling east at 19.0 km/s while descending at a rate of 12.9 km/s. What is its speed, in km/s?

To find the speed of the meteoroid, we need to use the concept of vector addition. The meteoroid is moving both eastward and downward, so we can treat these two motions as perpendicular components of its velocity.

We can use the Pythagorean theorem to find the magnitude of the velocity vector. The Pythagorean theorem states that the square of the hypotenuse (c) of a right triangle is equal to the sum of the squares of the other two sides (a and b).

In this case, the eastward speed (19.0 km/s) represents one side of the right triangle, while the downward speed (12.9 km/s) represents the other side.

So, let's apply the Pythagorean theorem to find the magnitude (speed) of the meteoroid:

speed = √(eastward speed^2 + downward speed^2)
= √(19.0 km/s)^2 + (12.9 km/s)^2)

Calculating this equation:

speed = √(361 km^2/s^2 + 166.41 km^2/s^2)
= √(527.41 km^2/s^2)
= 22.98 km/s

Therefore, the speed of the meteoroid is approximately 22.98 km/s.