Question

Solve for the resultant displacement of the two vectors: A = 2.3 km at 45 degrees B = 4.8 km at 90 degrees

Answer 1

Answer:

The resultant of the vector is 6.63 km

Explanation:

Given;

vector A = 2.3 km 45°

vector B = 4.8 km 90°

The vectors in the x - direction is given by;

Aₓ = 2.3 km Cos 45° = 1.6263 km

Bₓ = 4.8 km Cos 90° = 0

The sum of the vectors in x -direction is given by;

∑X =  1.6263 km + 0 = 1.6263 km

The vectors in the y - direction is given by;

Ay = 2.3 km Sin 45 = 1.6263 km

By = 4.8 km Sin 90° = 4.8 km

The sum of the vectors in y -direction is given by;

∑Y =  1.6263 km + 4.8 km = 6.4263 km

The resultant vector is given by;

R = √(X² + Y²)

R = √[(1.6263)² + (6.4263)²]

R = 6.63 km

Therefore, the resultant of the vector is 6.63 km