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You are a jungle scientist. Your boss gives you the following alligator dive diagram. Your boss informs you of some key information. The gator travels at the top of the swamp surface 100m west and then 90.0m in a direction 33.0 degrees to the east of north. Then the gator dives below the swamp surface and travels an additional distance in an unknown direction. The final location of the gator is 60.0 m directly under a float marker which is placed 125m north of the gator's start location. Find what the gator's displacement was during this gator dive. www ALIGATOR DIVE DIAGRAM East APA 4 North 60m 120m

You are a jungle scientist. Your boss gives you the following alligator dive diagram. Your boss informs you of some key information. The gator travels at the top of the swamp surface 100m west and then 90.0m in a direction 33.0 degrees to the east of north. Then the gator dives below the swamp surface and travels an additional distance in an unknown direction. The final location of the gator is 60.0 m directly under a float marker which is placed 125m north of the gator's start location. Find what the gator's displacement was during this gator dive. www ALIGATOR DIVE DIAGRAM East APA 4 North 60m 120m

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**Alligator Dive Displacement Analysis** **Scenario:** You are a jungle scientist, and your boss has provided you with a detailed alligator dive diagram. According to the information given: 1. The alligator moves 100 meters west along the swamp's surface. 2. It then proceeds to travel 90 meters in a direction 33 degrees east of north. 3. Subsequently, the alligator dives below the swamp's surface, covering an additional distance in an unknown direction. 4. The final location of the alligator is exactly 60 meters directly under a float marker stationed 125 meters north of its starting point. Your task is to find the total displacement of the alligator during its dive. **Annotated Dive Diagram:** - **Labels and Vectors:** - The initial position of the gator (starting point) is denoted as point \( A \). - Point \( B \) marks the position after traveling 100 meters west. - Point \( C \) represents the position after moving 90 meters, 33 degrees east of north from point \( B \). - The final position of the gator at point \( D \), comprising an unknown underwater distance directly below a float located 125 meters north from the start, is 60 meters directly beneath the float marker. **Steps & Calculation:** - **Step 1: Analyzing surface travel:** - Initial westward travel: \( 100 \) meters to the west. - Travel at an angle: \( 90 \) meters at \( 33° \) to the east of north. - **Step 2: Position Calculation:** - Decompose the \( 90 \)-meter vector: - Northward component: \( 90 \times \cos(33°) \) - Eastward component: \( 90 \times \sin(33°) \) - Resulting position \( C \): - North vector: \( 90 \times \cos(33°) \) - Net West vector: \( 100 - 90 \times \sin(33°) \) - **Step 3: Determining final displacement:** - The final position is 125 meters north (vertical displacement: \(60m\) downward). - Vector analysis to ascertain the straight-line displacement from start to end \( \textbf{D} ( \sqrt{(100 -
Transcribed Image Text:**Alligator Dive Displacement Analysis** **Scenario:** You are a jungle scientist, and your boss has provided you with a detailed alligator dive diagram. According to the information given: 1. The alligator moves 100 meters west along the swamp's surface. 2. It then proceeds to travel 90 meters in a direction 33 degrees east of north. 3. Subsequently, the alligator dives below the swamp's surface, covering an additional distance in an unknown direction. 4. The final location of the alligator is exactly 60 meters directly under a float marker stationed 125 meters north of its starting point. Your task is to find the total displacement of the alligator during its dive. **Annotated Dive Diagram:** - **Labels and Vectors:** - The initial position of the gator (starting point) is denoted as point \( A \). - Point \( B \) marks the position after traveling 100 meters west. - Point \( C \) represents the position after moving 90 meters, 33 degrees east of north from point \( B \). - The final position of the gator at point \( D \), comprising an unknown underwater distance directly below a float located 125 meters north from the start, is 60 meters directly beneath the float marker. **Steps & Calculation:** - **Step 1: Analyzing surface travel:** - Initial westward travel: \( 100 \) meters to the west. - Travel at an angle: \( 90 \) meters at \( 33° \) to the east of north. - **Step 2: Position Calculation:** - Decompose the \( 90 \)-meter vector: - Northward component: \( 90 \times \cos(33°) \) - Eastward component: \( 90 \times \sin(33°) \) - Resulting position \( C \): - North vector: \( 90 \times \cos(33°) \) - Net West vector: \( 100 - 90 \times \sin(33°) \) - **Step 3: Determining final displacement:** - The final position is 125 meters north (vertical displacement: \(60m\) downward). - Vector analysis to ascertain the straight-line displacement from start to end \( \textbf{D} ( \sqrt{(100 -
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