Domanda del libro di testo
Jack and Jill ran up the hill at 3.0 m/s. The horizontal component of Jill's velocity vector was 2.5 m/s. What was the vertical component of Jill's velocity?
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Ch 03: Vectors and Coordinate Systems
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796
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TOC.tableOfContents
- Ch 01: Concepts of Motion35
- Ch 02: Kinematics in One Dimension75
- Ch 03: Vectors and Coordinate Systems58
- Ch 04: Kinematics in Two Dimensions60
- Ch 05: Force and Motion23
- Ch 06: Dynamics I: Motion Along a Line53
- Ch 07: Newton's Third Law27
- Ch 08: Dynamics II: Motion in a Plane52
- Ch 09: Work and Kinetic Energy56
- Ch 10: Interactions and Potential Energy50
- Ch 11: Impulse and Momentum56
- Ch 12: Rotation of a Rigid Body71
- Ch 13: Newton's Theory of Gravity52
- Ch 14: Fluids and Elasticity44
- Ch 15: Oscillations55
- Ch 16: Traveling Waves37
- Ch 17: Superposition39
- Ch 18: A Macroscopic Description of Matter53
- Ch 19: Work, Heat, and the First Law of Thermodynamics60
- Ch 20: The Micro/Macro Connection53
- Ch 21: Heat Engines and Refrigerators34
- Ch 22: Electric Charges and Forces40
- Ch 23: The Electric Field39
- Ch 24: Gauss' Law32
- Ch 25: The Electric Potential63
- Ch 26: Potential and Field57
- Ch 27: Current and Resistance42
- Ch 28: Fundamentals of Circuits39
- Ch 29: The Magnetic Field47
- Ch 30: Electromagnetic Induction60
- Ch 31: Electromagnetic Fields and Waves32
- Ch 32: AC Circuits63
- Ch 33: Wave Optics32
- Ch 34: Ray Optics57
- Ch 35: Optical Instruments30
- Ch 36: Special Relativity38
- Ch 37: The Foundations of Modern Physics25
- Ch 38: Quantization49
- Ch 39: Wave Functions and Uncertainty31
- Ch 40: One-Dimensional Quantum Mechanics35
- Ch 41: Atomic Physics18
- Ch 42: Nuclear Physics27
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Non è quello che usi tu?Cambia libro di testo
Capitolo 3, Problema 34
You are fixing the roof of your house when a hammer breaks loose and slides down. The roof makes an angle of 35° with the horizontal, and the hammer is moving at 4.5 m/s when it reaches the edge. What are the horizontal and vertical components of the hammer's velocity just as it leaves the roof?
Guida verificata passo dopo passo1
Step 1: Understand the problem. The hammer is sliding down a roof inclined at an angle of 35° with the horizontal. Its velocity at the edge of the roof is 4.5 m/s. We need to find the horizontal and vertical components of this velocity.
Step 2: Recall the relationship between the components of velocity and the angle of inclination. The horizontal component of velocity (v_x) is given by v_x = v * cos(θ), and the vertical component of velocity (v_y) is given by v_y = v * sin(θ), where v is the magnitude of the velocity and θ is the angle of inclination.
Step 3: Substitute the given values into the formulas. The magnitude of the velocity (v) is 4.5 m/s, and the angle of inclination (θ) is 35°. Use the trigonometric functions cosine and sine to calculate the components.
Step 4: For the horizontal component, use the formula v_x = 4.5 * cos(35°). Ensure that the angle is in degrees if using a calculator or convert to radians if required by your calculation method.
Step 5: For the vertical component, use the formula v_y = 4.5 * sin(35°). Again, ensure the angle is correctly interpreted by your calculation method. These two components represent the hammer's velocity in the horizontal and vertical directions as it leaves the roof.
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Vector Components
In physics, a vector can be broken down into its horizontal and vertical components. This is essential for analyzing motion in two dimensions. The horizontal component is found by multiplying the vector's magnitude by the cosine of the angle, while the vertical component is found by multiplying by the sine of the angle. This decomposition allows for easier calculations of motion in different directions.
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Percorso guidato
07:30
Vector Addition By Components
Trigonometric Functions
Trigonometric functions, specifically sine and cosine, relate the angles of a triangle to the ratios of its sides. In this context, they are used to determine the components of the hammer's velocity based on the angle of the roof. For an angle θ, the cosine function gives the adjacent side (horizontal component), and the sine function gives the opposite side (vertical component). Understanding these functions is crucial for solving problems involving angles and motion.
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Percorso guidato
08:30Intro to Wave Functions
Kinematics
Kinematics is the branch of physics that describes the motion of objects without considering the forces that cause the motion. It involves concepts such as velocity, acceleration, and displacement. In this scenario, kinematics helps us analyze the hammer's motion as it transitions from the roof to free fall, allowing us to calculate its velocity components at the moment it leaves the roof.
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Percorso guidato
08:25Kinematics Equations
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