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WAEC SSCE - Physics - 1999 (Objective)

Question 1 Report

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 end of the 6s his displacement from the road junction is 50m in the direction of
Answer Details
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 N53oE. Therefore, the answer is (a) N53oE.