Question Part Points Submissions Used Mariana finds a cave to explore. Starting

Question

Question Part Points Submissions Used Mariana finds a cave to explore. Starting at the cave entrance, Mariana first follows a passage 75.0 m north, then turns and moves 250 m east, then goes 122 m at an angle 30.0° north of east, and finally moves 190 m south. Find the resultant displacement from the cave entrance. Shown is a sketch of the situation not drawn to scale. (Give the magnitude of the displacement in m and the direction in degrees south of east.)

What is the resultant displacement from the entrance?

magnitude = m

direction= ° south of east

Explanation / Answer

r1 = 75j m

r2 = 250i m

r3 = 122(cos30i + sin30j) = 105.7i + 61j m

r4 = - 190 j

r = r1 + r2 + r3 + r4

r = 355.7i - 54j m

magnitude = sqrt[ 355.7^2 + (-54)^2]

= 360 m ........Ans

Direction = tan^-1(54 / 355.7) = 9 deg ....Ans

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