physics

posted by .

A spelunker is surveying a cave. She follows a passage 150m straight west, then 270m in a direction 45^\circ east of south, and then 280 {\rm m} at 30^\circ east of north. After a fourth unmeasured displacement, she finds herself back where she started.Use a scale drawing to determine the magnitude of the fourth displacement?

• physics -

After doing all the calculations below, I just realized you just needed a scale drawing.
Oh, well, no harm done
Get a nice sheet of graph paper, scale the units to the following
150 m --> 15/2 = 7.5 cm
270 m --> 27/2 = 13.5 cm
280 m --> 28/2 = 14 cm , to fit on a standard sheet of paper.

You will need a compass and a protractor.

Most of your sketch will be in the third and fourth quadrant of the grid, so put your origin near the top part of the graph paper about 1/2 of the way over.

1. from your origin, draw a horizontal line 7.5 cm long
2. at the end of that line draw a line down at S 45°E.
3. set your compass to 13.5 cm and mark off that line
4. from that end point, draw a line making an angle of 75° with the previous line
5. set your compass to 14 cm and mark off this new line.
6. Join this point to the origin
7. measure that line, it should be appr. 9.2 cm (if my work below does not contain any stupid arithmetic errors).

I think we can solve this using vectors.
any vector (x,y) can be described by (rcosØ, rsinØ), where r is its magnitude and Ø is the angle it forms with the positive x-axis
so we have to convert our different paths
150m straight west --> (150cos180, 150sin180) = (-150, 0)
270m in a direction 45^\circ east of south
= (270cos315°, 270sin315) = (190.919 , -190.919)
280 {\rm m} at 30^\circ east of north
= (280cos60, 280sin60) = (140 , 242.49)

so (-150, 0) + (190.919 , -190.919) + (140 , 242.49) + (x,y) = (0,0)

-150 + 190.919 + 140 + x = 0
x = -180.919

0 -190.919 + 242.49 + y = 0
y = -51.571

(x,y) = (-180.919, -51.571)
magnitude = √(x^2 + y^2) = 188.13 m or 188 m to the nearest metre

Similar Questions

1. Physics

while surveying a cave, a spelunker follows a passge 180m straight west, then 210 m in a direction 45 degrees east of south and then 280m at 30.0 degrees east of north. After a fourth unmeasured displacement, she finds herself back …
2. physics

While exploring a cave, a spelunker starts at the entrance and moves the following distances: 75.0 m north, 275 m east, 215 m at an angle 30.0° north of east, and 150 m south. Find the resultant displacement from the cave entrance.
3. physics

While exploring a cave, a spelunker starts at the entrance and moves the following distances: 75.0 m north, 245 m east, 210 m at an angle 30.0° north of east, and 150 m south. Find the resultant displacement from the cave entrance.
4. physics

While exploring a cave, a spelunker starts at the entrance and moves the following distances: 75.0 m north, 225 m east, 160 m at an angle 30.0° north of east, and 150 m south. Find the resultant displacement from the cave entrance.
5. physics

A 40.0 kg crate is initially moving with a velocity that has magnitude 4.09 m/s in a direction 37.0 ^\circ west of north. How much work must be done on the crate to change its velocity to 5.49 m/s in a direction 63.0 ^\circ south of …
6. physics

A spelunker is surveying a cave. She follows a passage 120 m straight west, then 210 m in a direction 45∘ east of south, and then 280 m at 30∘ east of north. After a fourth unmeasured displacement, she finds herself back …
7. physics

A spelunker is surveying a cave. She follows a passage 140 m straight west, then 250 m in a direction 45∘ east of south, and then 280 m at 30∘ east of north. After a fourth unmeasured displacement, she finds herself back …
8. science

While exploring a cave, a spelunker starts at the entrance and moves the following distances. She goes 75.0 m north, 250 m east, 109 m at an angle θ = 30.0° north of east, and 156 m south. Find the resultant displacement from …
9. physics vectors

While exploring a cave, a spelunker starts at the entrance and moves the following distances. She goes 75.0 m north, 250 m east, 109 m at an angle θ = 30.0° north of east, and 156 m south. Find the resultant displacement from …
10. Science

A cave explorer is surveying the cave. He follows a passage 100m straight east, then 50m in the direction 30degree west of north, then 150m at 45degree west of south. After fourth unmeasured displacement he finds himself back where …

More Similar Questions