Textbook Question
A large boulder is ejected vertically upward from a volcano with an initial speed of m/s. Ignore air resistance. When is the velocity of the boulder zero?
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Ch 02: Motion Along a Straight Line
Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610
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Table of contents
- Ch 01: Units, Physical Quantities & Vectors41
- Ch 02: Motion Along a Straight Line67
- Ch 03: Motion in Two or Three Dimensions47
- Ch 04: Newton's Laws of Motion23
- Ch 05: Applying Newton's Laws59
- Ch 06: Work & Kinetic Energy14
- Ch 07: Potential Energy & Conservation8
- Ch 08: Momentum, Impulse, and Collisions18
- Ch 09: Rotation of Rigid Bodies42
- Ch 10: Dynamics of Rotational Motion48
- Ch 11: Equilibrium & Elasticity27
- Ch 12: Fluid Mechanics31
- Ch 13: Gravitation35
- Ch 14: Periodic Motion32
- Ch 15: Mechanical Waves25
- Ch 16: Sound & Hearing32
- Ch 17: Temperature and Heat36
- Ch 18: Thermal Properties of Matter38
- Ch 19: The First Law of Thermodynamics33
- Ch 20: The Second Law of Thermodynamics22
- Ch 21: Electric Charge and Electric Field36
- Ch 22: Gauss' Law24
- Ch 23: Electric Potential31
- Ch 24: Capacitance and Dielectrics18
- Ch 25: Current, Resistance, and EMF26
- Ch 26: Direct-Current Circuits30
- Ch 27: Magnetic Field and Magnetic Forces18
- Ch 28: Sources of Magnetic Field10
- Ch 29: Electromagnetic Induction28
- Ch 30: Inductance17
- Ch 31: Alternating Current21
- Ch 32: Electromagnetic Waves1
- Ch 33: The Nature and Propagation of Light20
- Ch 34: Geometric Optics34
- Ch 35: Interference19
- Ch 36: Diffraction25
- Ch 37: Special Relativity20
- Ch 38: Photons: Light Waves Behaving as Particles15
- Ch 39: Particles Behaving as Waves26
- Ch 40: Quantum Mechanics I: Wave Functions21
- Ch 41: Quantum Mechanics II: Atomic Structure25
- Ch 42: Molecules and Condensed Matter18
- Ch 43: Nuclear Physics16
- Ch 44: Particle Physics and Cosmology23
Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610Not the one you use?Change textbook
Chapter 2, Problem 48e
A large boulder is ejected vertically upward from a volcano with an initial speed of m/s. Ignore air resistance. What are the magnitude and direction of the acceleration while the boulder is (i) moving upward? (ii) Moving downward? (iii) At the highest point?
Verified step by step guidance1
Identify the forces acting on the boulder: Since the problem states to ignore air resistance, the only force acting on the boulder is gravity.
Understand the concept of acceleration due to gravity: Regardless of the direction of motion, the acceleration due to gravity near the Earth's surface is constant and directed downward. This is approximately 9.8 m/s².
Determine the acceleration while moving upward: As the boulder moves upward, it is decelerating due to gravity. The magnitude of the acceleration is 9.8 m/s², and the direction is downward.
Determine the acceleration while moving downward: As the boulder moves downward, it is accelerating due to gravity. The magnitude of the acceleration remains 9.8 m/s², and the direction is still downward.
Determine the acceleration at the highest point: At the highest point, the boulder's velocity is momentarily zero, but the acceleration due to gravity is still present. The magnitude is 9.8 m/s², and the direction is downward.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Gravitational Acceleration
Gravitational acceleration is the constant acceleration experienced by an object due to Earth's gravity, approximately 9.8 m/s² downward. Regardless of the object's motion direction, this acceleration remains constant, affecting the boulder's upward, downward, and peak motion.
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Projectile Motion
Projectile motion involves objects moving under the influence of gravity alone, following a parabolic trajectory. In this scenario, the boulder is a projectile, initially moving upward, slowing down until it reaches its peak, then accelerating downward, all under constant gravitational acceleration.
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Velocity at the Highest Point
At the highest point of its trajectory, the boulder's vertical velocity becomes zero momentarily before it starts descending. Despite the velocity being zero, gravitational acceleration still acts downward, preparing the boulder to accelerate back towards the ground.
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Related Practice
Textbook Question
A rocket starts from rest and moves upward from the surface of the earth. For the first s of its motion, the vertical acceleration of the rocket is given by m/s3, where the -direction is upward. What is the height of the rocket above the surface of the earth at s?
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Textbook Question
A large boulder is ejected vertically upward from a volcano with an initial speed of m/s. Ignore air resistance. At what time is it moving at m/s downward?
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Textbook Question
A large boulder is ejected vertically upward from a volcano with an initial speed of m/s. Ignore air resistance. When is the displacement of the boulder from its initial position zero?
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Textbook Question
A rocket starts from rest and moves upward from the surface of the earth. For the first s of its motion, the vertical acceleration of the rocket is given by m/s3, where the -direction is upward. What is the speed of the rocket when it is m above the surface of the earth?
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Textbook Question
You throw a small rock straight up from the edge of a highway bridge that crosses a river. The rock passes you on its way down, s after it was thrown. What is the speed of the rock just before it reaches the water m below the point where the rock left your hand? Ignore air resistance.
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