A motorcyclist, passing a road junction, moves due west for 8 s at a uniform speed of 5ms-1. He then moves due north for another 6 s with the same speed. At...

The motorcyclist travels west for 8 seconds at a speed of 5 m/s, so his distance traveled is: distance = speed × time = 5 m/s × 8 s = 40 m Next, he turns and travels north for 6 seconds at the same speed of 5 m/s. His distance traveled in the north direction is: distance = speed × time = 5 m/s × 6 s = 30 m To find the displacement from the road junction, we need to use the Pythagorean theorem because the displacement is the straight-line distance between the starting point and the ending point. The displacement is the hypotenuse of a right-angled triangle with the westward distance as one side and the northward distance as the other side. Using the Pythagorean theorem: displacement² = (40 m)² + (30 m)² = 1600 m² + 900 m² = 2500 m² displacement = √(2500 m²) = 50 m Thus, the motorcyclist's displacement from the road junction is 50 m. The displacement is in the direction of the hypotenuse of the right-angled triangle, which can be found using trigonometry. The angle is given by: tan θ = opposite / adjacent = 40 m / 30 m θ = tan^-1(40/30) = 53.13° Since the motorcyclist moved north after moving west, the direction of displacement from the road junction is N53^oE. Therefore, the answer is (a) N53^oE.