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 can use the Pythagorean theorem. The Pythagorean 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 eastward speed of the meteoroid is 14.8 km/s, and the downward speed is 12.5 km/s. These speeds can be considered as the two sides of a right triangle.
Using the Pythagorean theorem, we can find the hypotenuse (the speed of the meteoroid) as follows:
speed^2 = (eastward speed)^2 + (downward speed)^2
speed^2 = (14.8 km/s)^2 + (12.5 km/s)^2
speed^2 = 219.04 km^2/s^2 + 156.25 km^2/s^2
speed^2 = 375.29 km^2/s^2
To find the speed, we take the square root of both sides:
speed = √(375.29 km^2/s^2)
speed ≈ 19.36 km/s
Therefore, the speed of the meteoroid is approximately 19.36 km/s.