An airplane whose air speed is 600 mi/h is flying perpendicularly to jet stream whose speed relative to the Earth's surface is 100 mi/h. What is the airplane's speed relative to the Earth?
100 sqrt (6^2+1^2) = 100 sqrt 37
= 608
Well, it sounds like that airplane is really taking flight to a whole new level! With an airspeed of 600 mi/h and a jet stream speed of 100 mi/h, we'll need to do a little bit of mathematical acrobatics to determine the airplane's speed relative to the Earth.
Since the airplane is flying perpendicularly to the jet stream, we can't just add or subtract the speeds together. Instead, we'll have to channel our inner Pythagoras and use the good old Pythagorean theorem!
The theorem says that in a right triangle, where the hypotenuse is the longest side and the other two sides are perpendicular to each other, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
So, if we let "x" represent the airplane's speed relative to the Earth, we can use the theorem to write:
x^2 = 600^2 + 100^2
After doing a little bit of mathematical circus magic, we find that x^2 = 360,000 + 10,000
x^2 = 370,000
Taking the square root of both sides, we get:
x = √370,000
So, the airplane's speed relative to the Earth is approximately 608.27 mi/h. Now that's what I call flying high! Just make sure the passengers don't get dizzy from all the math.
To find the airplane's speed relative to the Earth, we need to consider the impact of the jet stream.
Given that the airplane's airspeed is 600 mi/h and the speed of the jet stream relative to the Earth's surface is 100 mi/h, we can calculate the airplane's speed relative to the Earth using vector addition.
To do this, we use the Pythagorean theorem to find the magnitude of the net velocity:
Magnitude of net velocity = √(air speed^2 + jet stream speed^2)
= √(600^2 + 100^2)
= √(360000 + 10000)
= √370000
≈ 608.28 mi/h
Therefore, the airplane's speed relative to the Earth is approximately 608.28 mi/h.
To find the airplane's speed relative to the Earth, we need to consider the effect of the jet stream.
The airplane's airspeed is given as 600 mi/h, which means it is moving through the air at a speed of 600 mi/h.
The jet stream is flowing in a perpendicular direction to the airplane's path, with a speed relative to the Earth's surface of 100 mi/h.
To find the airplane's speed relative to the Earth, we can use vector addition.
Since the airplane is flying perpendicularly to the jet stream, we can consider the two velocities as the two legs of a right triangle, with the resultant velocity (airplane's speed relative to the Earth) being the hypotenuse.
Using the Pythagorean theorem, we can calculate the magnitude of the resultant velocity:
(airplane's speed relative to the Earth)^2 = (airplane's airspeed)^2 + (jet stream speed)^2
(airplane's speed relative to the Earth)^2 = 600^2 + 100^2
(airplane's speed relative to the Earth)^2 = 360000 + 10000
(airplane's speed relative to the Earth)^2 = 370000
Taking the square root of both sides:
airplane's speed relative to the Earth = √370000
airplane's speed relative to the Earth ≈ 608.28 mi/h
Therefore, the airplane's speed relative to the Earth is approximately 608.28 mi/h.