Question

An aeroplane is heading northeast at a speed of 141.4m/s the northward component of velocity is

Answer 1

An aeroplane is heading north-east at a speed of 141.4 ms-1. The northward component of its velocity is...

solution : at first, we should write vector form of velocity of aeroplane.

as it is given that, speed of aeroplane is directed to North - east. means, velocity makes an angle of 45° with the east (+x-axis)

so, velocity of aeroplane ,

= 141.4(1/√2 i + 1/√2 j )

[ as we know, √2 = 1.414 ]

so, v = (141.4/1.414) i + (141.4/1.414)j

= 100i + 100j

[ here you should keep in your mind, 100i is the component of velocity vector along north direction (positive x-axis) and 100j is the component of velocity vector along south direction (positive y-axis)

hence, northward component (i.e., j) of the velocity of aeroplane is 100 m/s.

short cut : 141.4sin45° = 141.4 × 1/1.414 = 100m/s