Phys 1 with calculus 1.While exploring a cave, a spelunker starts at the entranc

Question

Phys 1 with calculus

1.While exploring a cave, a spelunker starts at the entrance and moves the following distances. She goes 75.0 m north, 250. m east, 120. m at an angle 30.0° north of east, and 165 m south. Find the resultant displacement from the cave entrance.
Magnitude
_________
Direction ° _____

south of east or north of east ?

2. A plane flies from base camp to Lake A, 250. km away in the direction 20.0° north of east. After dropping off supplies it flies to Lake B, which is 145 km at 30.0° west of north from Lake A. Determine the distance and direction FROM Lake B TO the base camp.

Explanation / Answer

1)

we solve this problem with using vector so

1st vector = 75 m j

2nd vector = 250 m i

3rd vector = 120*cos30 i + 120*sin30 j = 103.92 m i + 60 m j

and 4th vector = - 165 m j

now for resultant displacement we add all vectors (R) = 75 m j + 250 m i + 103.92 m i + 60 m j - 165 m j

R = 353.92 i - 30 j

magnitude = sqrt(353.92^2 + 30^2) = 355.19 m

direction = arctan(-30/353.92) = 4.84 degress south of east

2)

Using vector representation

vector A = 250*cos20 i + 250*sin20 = 234.92 km i + 85.5 km j

vector B = 145*cos(90+30) i + 145*sin(90+30) j = - 72.5 km i + 125.57 km j

Resultant = A + B = 234.92 km i - 72.5 km i + 85.5 km j + 125.57 km j

Resultant = 162.42 km i + 211.07 km j

Distance = magnitude of R = sqrt(162.42^2 + 211.07^2) = 266.32 km

direction = arctan(211.07/162.42) = 52.42 degrees north of east

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