meteoroid is speeding through the atmosphere, traveling east at 17.0 km/s while descending at a rate of 11.7 km/s. What is its speed, in km/s?
v=√(v⒳² +v⒴²) =
=√(17²+11.7²) =20.64 km/s
To determine the speed of the meteoroid, we can use the Pythagorean theorem, which states that the square of the hypotenuse (the speed) is equal to the sum of the squares of the other two sides. In this case, the horizontal speed (eastward) is 17.0 km/s, and the downward speed is 11.7 km/s.
So, using the Pythagorean theorem, we can calculate the speed of the meteoroid as follows:
Speed = sqrt((horizontal speed)^2 + (downward speed)^2)
= sqrt((17.0 km/s)^2 + (11.7 km/s)^2)
= sqrt(289 km^2/s^2 + 136.89 km^2/s^2)
= sqrt(425.89 km^2/s^2)
≈ 20.64 km/s
Therefore, the speed of the meteoroid is approximately 20.64 km/s.
To find the speed of the meteoroid in this scenario, we can use the Pythagorean theorem. The horizontal speed (eastward) and vertical speed (descending) form the legs of a right triangle, while the total speed acts as the hypotenuse.
Using the Pythagorean theorem, we have:
Total speed^2 = Horizontal speed^2 + Vertical speed^2
Let's calculate it step by step:
Horizontal speed = 17.0 km/s
Vertical speed = 11.7 km/s
Plugging these values into the formula:
Total speed^2 = (17.0 km/s)^2 + (11.7 km/s)^2
Total speed^2 = 289 km^2/s^2 + 136.89 km^2/s^2
Total speed^2 = 425.89 km^2/s^2
Now, to find the total speed, we need to take the square root of both sides:
Total speed = √(425.89 km^2/s^2)
Total speed ≈ 20.64 km/s
Therefore, the speed of the meteoroid is approximately 20.64 km/s.