Physics vector

2012-09-29 8:46 pm

A spelunker is surveying a cave. She follows a passage 180m straight west, then
290m in a direction 45 degree east of south, and then 280m at 30 degree east of
north. After a fourth unmeasured displacement, she finds herself back where she
started.

a) determine the magnitude of the fourth displacement.

b) Determine the direction of the fourth displacement.

回答 (1)

天同

2012-09-29 10:48 pm

✔ 最佳答案

(a) Taking the North direction as +ve in the North-South line, and the East direction as +ve along the East-West line.

Net displacement in the North-South line
= [-290.sin(45) + 280.cos(30)] m
= 37.43 m

Net displacement along the East-West line
= [-180 +290.cos(45) + 280.sin(30)] m
= 165.06 m

Hence, magnitude of the 4th displacement
=square-root[37.43^2 + 165.06^2] m
= 169.25 m

(b) Angle at which the 4th displacement amkes with the North-South line
= arc-tan(165.06/37.43)
= 77.22 degrees
Hence, the direction of the 4th displacement is 77.22 degrees west of south.

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