Find the magnitude of the resultant of the following two vectors: i) 50 units due east and ii) 100 units 30° north of west.
the answer is 62 unit but how it come ?
To find the magnitude of the resultant of two vectors, we can use the vector addition.
First, let's represent the two given vectors visually:
i) 50 units due east: This vector can be represented as 50i, where i is the unit vector in the east direction.
ii) 100 units 30° north of west: This vector can be represented as 100(cos(150°)i + sin(150°)j), where cos(150°) represents the west component and sin(150°) represents the north component. Here, j is the unit vector in the north direction.
To find the resultant vector, we need to add these two vectors:
Resultant vector = 50i + 100(cos(150°)i + sin(150°)j)
Simplifying this expression:
Resultant vector = (50 + 100(cos(150°)))i + 100(sin(150°))j
Now, we can find the magnitude of the resultant vector using the Pythagorean theorem:
Magnitude of the resultant vector = sqrt((50 + 100(cos(150°)))^2 + (100(sin(150°)))^2)
Evaluating this expression:
Magnitude of the resultant vector = sqrt((50 + 100(-0.866))^2 + (100(0.5))^2)
Magnitude of the resultant vector = sqrt((50 - 86.6)^2 + (50)^2)
Magnitude of the resultant vector = sqrt(107.4^2 + 2500)
Magnitude of the resultant vector = sqrt(11551.76 + 2500)
Magnitude of the resultant vector ≈ sqrt(14051.76)
Magnitude of the resultant vector ≈ 118.63
Therefore, the magnitude of the resultant vector is approximately 118.63 units, not 62 units. It seems there might be an error in the given solution provided.