Question

20 km east plus 10 km northeast

Answer 1

Two vector addition:

Suppose given that Vector is R and it makes angle with +x-axis, then it's components are given by:

Rx = R*cos

Ry = R*sin

Using above rule: We need to add

20 km east + 10 km North east

A = 20 km east = 20 km at 0 deg from +x-axis

Ax = 20*cos 0 deg = 20 km

Ay = 20*sin 0 deg = 0 km

A = (20 i + 0 j) km

B = 10 km North-East = 10 km at 45 deg from +x-axis

Bx = 10*cos 45 deg = 7.07 km

By = 10*sin 45 deg = 7.07 km

B = (7.07 i + 7.07 j) km

Now Adding above two vectors

R = A + B = (20 i + 0 j) + (7.07 i + 7.07 j)

R = (20 + 7.07) i + (0 + 7.07) j

R = 27.07 i + 7.07 j

Magnitude of vector R will be:

|R| = sqrt (27.07^2 + 7.07^2) = 27.978 km = 28.0 km

Direction of vector R will be:

Direction = arctan (7.07/27.07) = 14.64 degree

So Vector R will be:

R = 28.0 km at 14.64 degree North of East