Textbook Question
A jet plane taking off from an aircraft carrier has acceleration a = ( 15 m/s², 22° above horizontal). What are the horizontal and vertical components of the jet's acceleration?
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Ch 03: Vectors and Coordinate Systems
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796
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Table of contents
- 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: 9780137344796Not the one you use?Change textbook
Chapter 3, Problem 35b
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?
Verified step by step guidance1
Identify the given values: The magnitude of Jill's velocity vector is 3.0 m/s, and the horizontal component of her velocity is 2.5 m/s.
Recall the Pythagorean theorem, which relates the components of a velocity vector to its magnitude: \( v^2 = v_x^2 + v_y^2 \), where \( v \) is the magnitude of the velocity, \( v_x \) is the horizontal component, and \( v_y \) is the vertical component.
Rearrange the equation to solve for the vertical component \( v_y \): \( v_y = \sqrt{v^2 - v_x^2} \).
Substitute the given values into the equation: \( v_y = \sqrt{(3.0 \ \text{m/s})^2 - (2.5 \ \text{m/s})^2} \).
Simplify the expression under the square root to find the vertical component of Jill's velocity.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Velocity Components
Velocity is a vector quantity that has both magnitude and direction. In two-dimensional motion, the velocity can be broken down into horizontal and vertical components. The horizontal component represents motion along the x-axis, while the vertical component represents motion along the y-axis. Understanding these components is essential for analyzing motion in different directions.
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Calculating Velocity Components
Pythagorean Theorem
The Pythagorean Theorem is a fundamental principle in geometry that relates the lengths of the sides of a right triangle. It states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. In the context of velocity, this theorem is used to calculate the resultant velocity when both horizontal and vertical components are known.
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Trigonometric Functions
Trigonometric functions, such as sine and cosine, relate the angles of a triangle to the ratios of its sides. In physics, these functions are often used to resolve vectors into their components. For example, the sine function can be used to find the vertical component of a velocity vector when the angle and the magnitude of the vector are known, which is crucial for solving problems involving inclined motion.
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Related Practice
Textbook Question
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 angle of the hill?
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Textbook Question
Kami is walking through the airport with her two-wheeled suitcase. The suitcase handle is tilted 40° from vertical, and Kami pulls parallel to the handle with a force of 120 N. (Force is measured in newtons, abbreviated N.) What are the horizontal and vertical components of her applied force?
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Textbook Question
A cannonball leaves the barrel with velocity v = (75î ＋ 45ĵ). At what angle is the barrel tilted above horizontal?
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Textbook Question
Your neighbor Paul has rented a truck with a loading ramp. The ramp is tilted upward at 25°, and Paul is pulling a large crate up the ramp with a rope that angles 10° above the ramp. If Paul pulls with a force of 550 N, what are the horizontal and vertical components of his force? (Force is measured in newtons, abbreviated N.)
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Textbook Question
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?
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