A jetliner is moving at a speed of 305 m/s. The vertical component of the plane's velocity is 38.9 m/s. Determine the magnitude of the horizontal component of the plane's velocity.
To find 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.
Let's call the horizontal component of the plane's velocity Vx and the vertical component Vy.
According to the given information, Vy = 38.9 m/s.
The total velocity of the plane, which is the hypotenuse of the right triangle formed by Vx and Vy, is given as 305 m/s.
Using the Pythagorean theorem, we can write the equation:
Vx^2 + Vy^2 = Vtotal^2
Substituting the known values:
Vx^2 + (38.9 m/s)^2 = (305 m/s)^2
Now, let's solve for Vx:
Vx^2 = (305 m/s)^2 - (38.9 m/s)^2
Vx^2 = 93025 m^2/s^2 - 1513.21 m^2/s^2
Vx^2 = 91511.79 m^2/s^2
Taking the square root of both sides, we have:
Vx = √(91511.79 m^2/s^2)
Vx ≈ 302.5 m/s
Therefore, the magnitude of the horizontal component of the plane's velocity is approximately 302.5 m/s.