Bob walks 260 m south, then jogs 870 msouthwest, then walks 260 m in a direction 30 degrees east ofnorth. Use components to find the displacement that will return Bobto his starting point by the most direct route. Give answerin distance. Find the direction of the displacement that will return Bob tohis starting point by the most direct route. Bob walks 260 m south, then jogs 870 msouthwest, then walks 260 m in a direction 30 degrees east ofnorth. Use components to find the displacement that will return Bobto his starting point by the most direct route. Give answerin distance. Find the direction of the displacement that will return Bob tohis starting point by the most direct route.
Explanation / Answer
Let the unit vector in east direction be i and in northdirection be j 1 st displacement S = 260 * ( -j ) = -260 j 2 nd displacement S ' = 870 cos 45 ( -i ) + 870 sin 45 (-j ) = - 615.18 i + 615.18 j 3 rd displacment S " = 260 sin 30 * i + 260 cos 30 *j = 130 i + 225.166 j total displacment s = S + S' + S" =-485.18 i + 580.34 j magnitude of displacment s = [ (-485.18 ) ^ 2 +580.34^ 2] = 756.34 m let the displacment makes an angle with west directionthen tan = (580.34 / 485.18 ) = 50.1 degrees angle with east direction = 180 - = 129.89degrees