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 after being ejected is the boulder moving at m/s upward?
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Ch 02: Motion Along a Straight Line
Young & Freedman Calc15th EditionUniversity PhysicsISBN: 9780135159552
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Table of contents
- Ch 01: Units, Physical Quantities & Vectors37
- Ch 02: Motion Along a Straight Line57
- Ch 03: Motion in Two or Three Dimensions45
- Ch 04: Newton's Laws of Motion23
- Ch 05: Applying Newton's Laws54
- Ch 06: Work & Kinetic Energy11
- Ch 07: Potential Energy & Conservation6
- Ch 08: Momentum, Impulse, and Collisions15
- Ch 09: Rotation of Rigid Bodies37
- Ch 10: Dynamics of Rotational Motion44
- Ch 11: Equilibrium & Elasticity27
- Ch 12: Fluid Mechanics27
- Ch 13: Gravitation34
- Ch 14: Periodic Motion26
- Ch 15: Mechanical Waves22
- Ch 16: Sound & Hearing28
- Ch 17: Temperature and Heat28
- Ch 18: Thermal Properties of Matter35
- Ch 19: The First Law of Thermodynamics29
- Ch 20: The Second Law of Thermodynamics18
- Ch 21: Electric Charge and Electric Field28
- Ch 22: Gauss' Law21
- Ch 23: Electric Potential31
- Ch 24: Capacitance and Dielectrics18
- Ch 25: Current, Resistance, and EMF24
- Ch 26: Direct-Current Circuits29
- Ch 27: Magnetic Field and Magnetic Forces16
- Ch 28: Sources of Magnetic Field10
- Ch 29: Electromagnetic Induction22
- Ch 30: Inductance14
- Ch 31: Alternating Current20
- Ch 33: The Nature and Propagation of Light17
- Ch 34: Geometric Optics29
- Ch 35: Interference13
- Ch 36: Diffraction19
- Ch 37: Special Relativity19
- Ch 38: Photons: Light Waves Behaving as Particles12
- Ch 39: Particles Behaving as Waves25
- Ch 40: Quantum Mechanics I: Wave Functions20
- Ch 41: Quantum Mechanics II: Atomic Structure21
- Ch 42: Molecules and Condensed Matter17
- Ch 43: Nuclear Physics13
- Ch 44: Particle Physics and Cosmology17
Young & Freedman Calc15th EditionUniversity PhysicsISBN: 9780135159552Not the one you use?Change textbook
Chapter 2, Problem 45
A -kg rock is dropped from rest on the earth and reaches the ground in s. When it is dropped from the same height on Saturn's satellite Enceladus, the rock reaches the ground in s. What is the acceleration due to gravity on Enceladus?
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Identify the known values for the problem on Earth: the mass of the rock (15 kg), the time it takes to reach the ground (1.75 s), and the acceleration due to gravity on Earth (9.81 m/s²).
Use the kinematic equation for free fall on Earth to find the height from which the rock is dropped: \( h = \frac{1}{2} g t^2 \), where \( g = 9.81 \text{ m/s}^2 \) and \( t = 1.75 \text{ s} \).
Calculate the height \( h \) using the values for Earth. This height will be the same for the drop on Enceladus.
Use the same kinematic equation for the drop on Enceladus: \( h = \frac{1}{2} g_{Enceladus} t^2 \), where \( t = 18.6 \text{ s} \) and \( h \) is the height calculated from the Earth scenario.
Solve for the acceleration due to gravity on Enceladus \( g_{Enceladus} \) by rearranging the equation: \( g_{Enceladus} = \frac{2h}{t^2} \). Substitute the known values to find \( g_{Enceladus} \).
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Acceleration due to Gravity
Acceleration due to gravity is the rate at which an object speeds up as it falls freely under the influence of gravity. On Earth, this is approximately 9.81 m/s². It varies depending on the celestial body, affecting how quickly objects fall.
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Acceleration Due to Gravity
Free Fall Motion
Free fall motion describes the movement of an object solely under the influence of gravity, without any air resistance. The time it takes for an object to reach the ground can be used to calculate the gravitational acceleration using kinematic equations.
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Kinematic Equations
Kinematic equations relate the variables of motion: displacement, initial velocity, final velocity, acceleration, and time. For an object in free fall, these equations can determine the acceleration due to gravity by using the time of fall and initial conditions.
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Related Practice
Textbook Question
An egg is thrown nearly vertically upward from a point near the cornice of a tall building. The egg just misses the cornice on the way down and passes a point m below its starting point s after it leaves the thrower's hand. Ignore air resistance. What is the magnitude of its velocity at the highest point?
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Textbook Question
An egg is thrown nearly vertically upward from a point near the cornice of a tall building. The egg just misses the cornice on the way down and passes a point m below its starting point s after it leaves the thrower's hand. Ignore air resistance. How high does it rise above its starting point?
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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
An egg is thrown nearly vertically upward from a point near the cornice of a tall building. The egg just misses the cornice on the way down and passes a point m below its starting point s after it leaves the thrower's hand. Ignore air resistance. What are the magnitude and direction of its acceleration at the highest point?
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