A jetliner is moving at a speed of 270 m/s. The vertical component of the plane's velocity is 39.8 m/s. Determine the magnitude of the horizontal component of the plane's velocity.
Can someone please solve this?
sqrt(270^2)+(39.8^2)
you should get 272m/s
To determine the magnitude of the horizontal component of the plane's velocity, 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 vertical component of the plane's velocity is one side of the right triangle, and the horizontal component of the plane's velocity is the other side. The magnitude of the velocity is the hypotenuse.
Using the Pythagorean theorem, the equation can be written as:
(velocity magnitude)^2 = (horizontal component)^2 + (vertical component)^2
We are given the vertical component of the velocity, which is 39.8 m/s.
We can solve for the magnitude of the velocity by rearranging the equation:
(velocity magnitude)^2 = (horizontal component)^2 + (39.8 m/s)^2
To find the magnitude of the horizontal component, rearrange the equation and solve for (horizontal component):
(horizontal component)^2 = (velocity magnitude)^2 - (39.8 m/s)^2
(horizontal component)^2 = (270 m/s)^2 - (39.8 m/s)^2
(horizontal component)^2 = 72900 m^2/s^2 - 1580.04 m^2/s^2
(horizontal component)^2 = 71319.96 m^2/s^2
Taking the square root of both sides, we get:
horizontal component = sqrt(71319.96 m^2/s^2)
Using a calculator, we find:
horizontal component ≈ 266.84 m/s
Therefore, the magnitude of the horizontal component of the plane's velocity is approximately 266.84 m/s.