An aircraft flies due East at a velocity of 120\text{ m/s} while a crosswind blows due Nor… — JAMB UTME

An aircraft flies due East at a velocity of $120\text{ m/s}$ while a crosswind blows due North at $50\text{ m/s}$ . What is the magnitude of the resultant velocity of the aircraft?

$130\text{ m/s}$ Answer
B
$170\text{ m/s}$
C
$70\text{ m/s}$
D
$110\text{ m/s}$

Answer

The magnitude of the resultant velocity of the aircraft is

130\text{ m/s}

Because the aircraft's velocity and the wind's velocity are perpendicular to each other, their vector sum is found using the Pythagorean theorem

R = \sqrt{v_1^2 + v_2^2}

. Substituting

120\text{ m/s}

and

50\text{ m/s}

gives

R = \sqrt{120^2 + 50^2} = \sqrt{16900} = 130\text{ m/s}

Step-by-Step Solution

Identify the given velocity vectors and their relative direction.

Velocity due East

\vec{v}_e = 120\text{ m/s}

and velocity due North

\vec{v}_n = 50\text{ m/s}

are perpendicular to each other (

90^\circ

angle).

East and North directions are orthogonal to each other.

Apply the Pythagorean theorem to calculate the magnitude of the resultant vector

R

R = \sqrt{v_e^2 + v_n^2} = \sqrt{120^2 + 50^2} = \sqrt{14400 + 2500} = \sqrt{16900} = 130\text{ m/s}

The resultant of two perpendicular vectors forms the hypotenuse of a right-angled triangle.

Key Concept

Vector Addition of Perpendicular Vectors

Estimated Time:1m 0s

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