# Find the resultant displacement from the cave entrance

• hawk24
In summary, the spelunker's resultant displacement from the cave entrance is 338.4173 meters at an angle of -5.93629 degrees. However, there may be a discrepancy with the given information as the calculated magnitude may differ from the expected value.
hawk24

## Homework Statement

While exploring a cave, a spelunker starts at the entrance and moves the following distances. She goes 75 m north, 250 m east, 100 m at an angle 30° north of east, and 160 m south. Find the resultant displacement from the cave entrance.

## The Attempt at a Solution

So (75+100sin30- 160) = -35
and 250 + 100cos30 = 336.6025
magnitude =338.4173

Trying to find the angle and should be arctan(-35/336.6025)=-5.93629

Here's my problme though I accidently used 150 m south and blackboard gave me credit for 335.6729 m as my magnitude. Now who is wrong me or blackboard? I'm at lost as to which numbers to use now for my angle calculation.

hi hawk24!

i'm surprised it didn't reject your answer as having too many sig figs …

maybe the correct answer is 340?

## 1. What is the meaning of "resultant displacement"?

Resultant displacement refers to the overall distance and direction of an object's movement or position from its starting point to its end point. It takes into account both the magnitude and direction of the individual displacements.

## 2. How do you calculate the resultant displacement?

The resultant displacement can be calculated using the Pythagorean theorem, where the magnitude of the resultant displacement is equal to the square root of the sum of the squares of the individual displacements. The direction can be determined using trigonometric functions such as tangent or sine.

## 3. Why is it important to find the resultant displacement from the cave entrance?

Finding the resultant displacement from the cave entrance is important because it gives us a clear understanding of the overall path and distance an object has traveled, which can be useful in various fields such as navigation, engineering, and physics.

## 4. What factors can affect the resultant displacement from the cave entrance?

The resultant displacement from the cave entrance can be affected by various factors such as the initial position of the object, the distance and direction of the individual displacements, external forces acting on the object, and any changes in the object's velocity or acceleration.

## 5. Can the resultant displacement from the cave entrance be negative?

Yes, the resultant displacement can be negative. This indicates that the object has moved in the opposite direction from its starting point. For example, if an object moves 5 meters east and then 3 meters west, the resultant displacement would be 2 meters west (negative).

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