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.
This is a Pythagorean theorem problem!
x^2+y^2=c^2
i.e. (horizontal component)^2 + (vertical component)^2 = (net component)^2
plug in the values that you know and solve for the horizontal component!
To determine the magnitude of the horizontal component of the plane's velocity, we need to use trigonometry. In this case, we can use the concept of vector components.
Let's assume that the vertical component of the plane's velocity is represented by Vy and the horizontal component of the plane's velocity is represented by Vx. The total velocity vector V can be represented as the combination of the vertical and horizontal components: V = (Vx, Vy).
We can use the Pythagorean theorem to find the magnitude (Vmag) of the total velocity vector V:
Vmag = √(Vx^2 + Vy^2)
Given that Vmag is 270 m/s and Vy is 39.8 m/s, we can rearrange the equation to solve for Vx:
270 = √(Vx^2 + 39.8^2)
Now, let's solve for Vx:
270^2 = Vx^2 + 39.8^2
72900 = Vx^2 + 1584.04
Vx^2 = 72900 - 1584.04
Vx^2 = 71315.96
Vx ≈ √71315.96
Vx ≈ 267.4 m/s
Therefore, the magnitude of the horizontal component of the plane's velocity is approximately 267.4 m/s.