A meteoroid is speeding through the atmosphere, traveling east at 15.5 km/s while descending at a rate of 10.6 km/s. What is its speed, in km/s?
V^2 = X^2 + Y^2 = 15.5^2 + 10.6^2
Solve for V.
To find the meteoroid's speed, we need to use vector addition. The meteoroid is traveling east at 15.5 km/s and descending at 10.6 km/s. Since the meteoroid is moving in two directions simultaneously, we can use the Pythagorean theorem to find the magnitude of its speed.
First, we square the magnitude of the eastward velocity:
(15.5 km/s)^2 = 240.25 km^2/s^2
Next, we square the magnitude of the downward velocity:
(10.6 km/s)^2 = 112.36 km^2/s^2
Next, we add these two squared values together:
240.25 km^2/s^2 + 112.36 km^2/s^2 = 352.61 km^2/s^2
Finally, we take the square root of this sum to find the magnitude of the meteoroid's speed:
√(352.61 km^2/s^2) ≈ 18.77 km/s
Therefore, the meteoroid's speed is approximately 18.77 km/s.