A meteoroid is speeding through the atmosphere, traveling east at 14.8 km/s while descending at a rate of 12.5 km/s. What is its speed, in km/s?
To find the speed of the meteoroid, we need to use the magnitude of its velocity vector. The velocity vector of the meteoroid can be separated into two components: the horizontal component (Eastward) and the vertical component (Descending).
Given:
Eastward velocity = 14.8 km/s
Descending velocity = 12.5 km/s
To find the magnitude of the velocity vector, we can use the Pythagorean theorem.
Magnitude of velocity vector = √(Eastward velocity^2 + Descending velocity^2)
Substituting the given values:
Magnitude of velocity vector = √((14.8 km/s)^2 + (12.5 km/s)^2)
Performing the calculation:
Magnitude of velocity vector = √(219.04 km^2/s^2 + 156.25 km^2/s^2)
= √375.29 km^2/s^2
≈ 19.37 km/s
Therefore, the speed of the meteoroid, in km/s, is approximately 19.37 km/s.