A body of mass 2 kg is moving on a smooth horizontal surface with initial…

When a net force acts perpendicular to a body's initial velocity, the two directions evolve completely independently: the component along the original direction is unaffected (no force acts there), while a new perpendicular component builds up from Newton's second law, a = F/m, together with v = u + at. The resultant velocity is then the vector sum of these two perpendicular components, found by the Pythagorean rule for magnitude and the inverse tangent for direction.

1. Set up perpendicular axes: east as the x-axis, north as the y-axis.

2. Along east (x): no force acts in this direction on the smooth horizontal surface, so the eastward velocity component stays constant at vx = 10 m/s throughout the 2 s.

3. Along north (y): the 10 N force gives an acceleration a = F/m = 10/2 = 5 m/s2. Starting from rest in this direction (uy = 0), after t = 2 s the northward component is vy = uy + at = 0 + 5×2 = 10 m/s.

4. Combine the two perpendicular components: resultant speed v = √(vx2 + vy2) = √(102 + 102) = √200 = 10√2 m/s.

5. Direction: θ = tan⁻¹(vy/vx) = tan⁻¹(10/10) = tan⁻¹(1) = 45°, measured from east towards north, i.e. 45° north of east.

Cross-check: since vx and vy are equal, the resultant must bisect the angle between east and north exactly, confirming 45° north of east rather than any south-of-east direction (the force has no southward or westward component at all). Also, a naive scalar sum of the two component magnitudes (10 + 10 = 20 m/s) is not physically valid here because the components are perpendicular vectors, not colinear speeds — they must be combined by vector addition, giving 10√2 m/s (≈14.14 m/s), not 20 m/s.