While exploring a cave, a spelunker starts at the entrance and moves the following distances: 75.0 m north, 275 m east, 160 m at an angle 30.0° north of east, and 150 m south. Find the resultant displacement from the cave entrance.

What School Subject is tsu?

The net north displacement is:

75 +80 sin 30 - 150 = -35. or 35 m south

The net eastward displacement is 275 + 160 cos 30 = 413.6 m

The total distance moved is given by
D^2 = (35)^2 + (413.6)^2

D = 415.0 m

To find the resultant displacement from the cave entrance, we can break down the spelunker's movements into their north-south and east-west components. We can then calculate the total displacement in each direction and combine them to determine the resultant displacement.

Let's start by calculating the north-south displacement. The spelunker moves 75.0 m north and then 150 m south. This means the total north-south displacement is 75.0 m - 150 m = -75.0 m (negative because it's south).

Next, let's calculate the east-west displacement. The spelunker moves 275 m east and then 160 m at an angle 30.0° north of east. To find the east-west component of this diagonal displacement, we need to calculate the cosine of the angle and multiply it by the distance. The east-west displacement is therefore 160 m * cos(30.0°) ≈ 138.56 m north of the east direction. When combined with the initial 275 m east movement, the total east-west displacement is 275 m + 138.56 m = 413.56 m.

Now we have both the north-south and east-west displacements. To find the resultant displacement, we can use the Pythagorean theorem, which states that the square of the resultant displacement is equal to the sum of the squares of the individual displacements.

Therefore, the resultant displacement^2 = (-75.0 m)^2 + (413.56 m)^2
resultant displacement^2 = 5625 m^2 + 171067.9936 m^2
resultant displacement^2 = 176692.9936 m^2

Taking the square root of both sides gives us the resultant displacement:
resultant displacement = √(176692.9936 m^2)
resultant displacement ≈ 420.58 m

Hence, the resultant displacement from the cave entrance is approximately 420.58 meters.