Question

While surveying a cave, a spelunker follows a passage 190 m straight west, then 220 m in a direction 45.0 ∘ east of south, and then 270 m at 30.0 ∘ east of north. After a fourth unmeasured displacement, she finds herself back where she started. Use vector components to find the magnitude and direction of the fourth displacement.

Answer 1

To find the magnitude and direction of the fourth displacement in a cave survey, vector components can be used. By breaking down the given displacements into their north and east components, calculating the net displacements, and using the Pythagorean theorem and trigonometry, the magnitude and direction of the fourth displacement can be determined.

Step-by-step explanation:

To find the magnitude and direction of the fourth displacement, we can use vector components. First, let's break down the given displacements into their north and east components:

Displacement 1: 190 m west (0 north, -190 east)

Displacement 2: 220 m at 45.0° east of south (-220 sin(45°) north, 220 cos(45°) east)

Displacement 3: 270 m at 30.0° east of north (270 sin(30°) north, 270 cos(30°) east)

Next, we can add up the north and east components separately to find the net north and east displacements. Lastly, we can use these net displacements to calculate the magnitude and direction of the fourth displacement using the Pythagorean theorem and trigonometry.

Answer 2

The magnitude of the displacement is 127.43m and the direction is 38°North of East

Step-by-step explanation: