Textbook Question
A 70.00 kg football player is gliding across very smooth ice at 2.00 m/s. He throws a 0.450 kg football straight forward. What is the player's speed afterward if the ball is thrown at 15.0 m/s relative to the ground?
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Ch 11: Impulse and Momentum
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 11, Problem 28
Dan is gliding on his skateboard at 4.0 m/s. He suddenly jumps backward off the skateboard, kicking the skateboard forward at 8.0 m/s. How fast is Dan going as his feet hit the ground? Dan's mass is 50 kg and the skateboard's mass is 5.0 kg.
Verified step by step guidance1
Identify the principle of conservation of momentum: The total momentum of the system (Dan and the skateboard) before the jump must equal the total momentum of the system after the jump, as no external forces act on the system.
Write the equation for the conservation of momentum: \( m_{Dan}v_{Dan,initial} + m_{skateboard}v_{skateboard,initial} = m_{Dan}v_{Dan,final} + m_{skateboard}v_{skateboard,final} \).
Substitute the known values into the equation: \( (50)(4.0) + (5.0)(4.0) = (50)v_{Dan,final} + (5.0)(8.0) \).
Simplify the equation to isolate \( v_{Dan,final} \): Combine terms on the left-hand side and simplify the right-hand side to solve for \( v_{Dan,final} \).
Solve for \( v_{Dan,final} \): Rearrange the equation to find Dan's final velocity, keeping in mind the direction of his velocity relative to the skateboard's motion.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Conservation of Momentum
The principle of conservation of momentum states that in a closed system, the total momentum before an event must equal the total momentum after the event, provided no external forces act on it. In this scenario, Dan and the skateboard form a closed system where the momentum before he jumps must equal the momentum after he jumps.
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05:58
Conservation Of Momentum
Momentum Calculation
Momentum is calculated as the product of an object's mass and its velocity (p = mv). For Dan and the skateboard, we can calculate their individual momenta before and after the jump to find Dan's final velocity. This involves using the masses and velocities of both Dan and the skateboard to set up an equation based on the conservation of momentum.
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05:17Intro to Momentum
Relative Velocity
Relative velocity refers to the velocity of one object as observed from another object. In this case, when Dan jumps backward off the skateboard, his velocity relative to the ground is affected by both his initial speed and the speed at which he kicks the skateboard forward. Understanding this concept helps in determining Dan's final speed as he leaves the skateboard.
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Related Practice
Textbook Question
A 50 g ball of clay traveling at speed v0 hits and sticks to a 1.0 kg brick sitting at rest on a frictionless surface. What is the speed of the brick after the collision?
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Textbook Question
An object at rest explodes into three fragments. FIGURE EX11.32 shows the momentum vectors of two of the fragments. What is the momentum of the third fragment? Write your answer using unit vectors.
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Textbook Question
A package of mass m is released from rest at a warehouse loading dock and slides down the 3.0-m-high, frictionless chute of FIGURE EX11.24 to a waiting truck. Unfortunately, the truck driver went on a break without having removed the previous package, of mass 2m, from the bottom of the chute. Suppose the collision between the packages is perfectly elastic. To what height does the package of mass m rebound?
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Textbook Question
At the center of a 50-m-diameter circular ice rink, a 75 kg skater traveling north at 2.5 m/s collides with and holds on to a 60 kg skater who had been heading west at 3.5 m/s. Where will they reach it? Give your answer as an angle north of west.
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Textbook Question
Two objects collide and bounce apart. FIGURE EX11.31 shows the initial momenta of both and the final momentum of object 2. What is the final momentum of object 1? Write your answer using unit vectors.
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