A jetliner is moving at a speed of 235 m/s. The vertical component of the plane's velocity is 34.3 m/s. Determine the magnitude of the horizontal component of the plane's velocity.
_____________m/s
Vo = 235m/s @ A-deg.
Yo = ver. = 34.3m/s.
sinA = Yo / r = 34.3 / 235 = 0.14595,
A = 8.393.
Xo = hor. = r*cosA = 235*cos8.393 = 232.5m/s.
To determine the magnitude of the horizontal component of the plane's velocity, we can use the Pythagorean theorem. This theorem states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
In this case, the vertical component of the velocity represents the length of one side of the right triangle, and the horizontal component of the velocity represents the length of the other side. The speed of the plane, which is the magnitude of the total velocity, represents the hypotenuse.
So, using the Pythagorean theorem, we have:
(speed of the plane)^2 = (vertical component of the velocity)^2 + (horizontal component of the velocity)^2
Plugging in the given values:
(235 m/s)^2 = (34.3 m/s)^2 + (horizontal component of the velocity)^2
Simplifying:
55125 m^2/s^2 = 1174.49 m^2/s^2 + (horizontal component of the velocity)^2
Subtracting 1174.49 m^2/s^2 from both sides:
(horizontal component of the velocity)^2 = 53950.51 m^2/s^2
Taking the square root of both sides:
horizontal component of the velocity = √53950.51 m/s
Calculating the square root:
horizontal component of the velocity ≈ 232.33 m/s
Therefore, the magnitude of the horizontal component of the plane's velocity is approximately 232.33 m/s.