Explanation Given data: Mass of the weather rocket ( m ) is 1500 kg. The rocket accelerates ( a y ) upward at 10.0 m s 2 . The rocket explodes 2.00 s after liftoff and breaks into two fragments. Mass of the heavier fragment is twice the lighter fragment. Therefore, consider the mass of the lighter fragment ( m L ) is 500 kg, and the heavier fragment ( m H ) is 1000 kg. The height reached by the lighter fragment y 3 is 530 m. Formula used: Refer to the (2.11) in the textbook, and modify the expression of kinematic equation for final velocity of a particle in vertical direction as follows. ( v y ) f = ( v y ) i + a y Δ t (1) Here, ( v y ) i is the initial velocity of the particle, a y is the acceleration of the particle, and Δ t is the duration of the acceleration period. Refer to the (2.12) in the textbook, and modify the expression of kinematic equation for final position of a particle in vertical direction as follows. y f = y i + ( v y ) i Δ t + 1 2 a y ( Δ t ) 2 (2) Here, y i is the initial position of the particle. Refer to the (2.13) in the textbook, and modify the expression of kinematic equation as follows. ( v y ) f 2 = ( v y ) i 2 + 2 a y Δ y (3) Here, Δ y is the distance between the particle’s initial and final position. From the given data, the rocket breaks into two fragments. As the two fragments stick together before the explosion, the collision is considered as inelastic collision. Write the expression for momentum of conservation for the given system as follows. m L ( v L ) f + m H ( v H ) f = ( m L + m H ) ( v ) i (4) Here, m L is the mass of the lighter fragment, m H is the mass of the heavier fragment, ( v L ) f is the final velocity of the lighter fragment, ( v H ) f is the final velocity of the heavier fragment, and ( v ) i is the initial velocity of the rocket (two fragments stick together before the collision). Explanation: From the given data, draw the constructive diagram for the given system as shown in Figure 1. In Figure 1, ( v y ) 0 is the velocity of the rocket at initial position, which is considered as 0 m s , y 0 is the height at which the rocket stays at initial position, t 0 is the instant at initial position of the rocket, a y is the acceleration of the rocket before it breaks, ( v y ) 1 is the velocity of the rocket at the instant of t 1 (time at the rocket breaks into two fragments), y 1 is the height at which the rocket breaks into two fragments, t 1 is the instant at which the rocket breaks into two fragments, y 2 is the height at which the lighter fragment at its initial position, t 2 is the instant at which the lighter fragment at its initial position, ( v L y ) 2 is the velocity of the lighter fragment just after the explosion, y 3 is the height at which the lighter fragment at its final position, t 3 is the instant at which the lighter fragment at its final position, ( v H y ) 2 is the velocity of the heavier fragment just after the explosion, which is to be determined, and ( v L y ) 2 is the velocity of the lighter fragment when it reaches to its final position, which is considered as 0 m s . Calculation of velocity of the rocket at the instant of t 1 [ ( v y ) 1 ] : Modify the expression in equation (1) for velocity of the rocket at the instant of t 1 as follows. ( v y ) 1 = ( v y ) 0 + a y Δ t Substitute 0 m s for ( v y ) 0 , 10.0 m s 2 for a y , and 2.00 s for Δ t , ( v y ) 1 = 0 m s + ( 10.0 m s 2 ) ( 2.00 s ) = 20 m s Calculation of height at which the rocket breaks into two fragments ( y 1 ) : Modify the expression in equation (2) to find the height at which the rocket breaks into two fragments as follows. y 1 = y 0 + ( v y ) 0 Δ t + 1 2 a y ( Δ t ) 2 Substitute 0 m for y 0 , 0 m s for ( v y ) 0 , 10

Pearson eText for College Physics: A Strategic Approach -- Instant Access (Pearson+)

4th Edition

ISBN: 9780137561520

Author: Randall Knight, Brian Jones

Publisher: PEARSON+

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Chapter 9, Problem 67GP

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To find: The speed and direction of the heavier fragment just after the explosion.

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Chapter 9, Problem 66GP

Chapter 9, Problem 69GP

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Chapter 9 Solutions

Pearson eText for College Physics: A Strategic Approach -- Instant Access (Pearson+)

Ch. 9 - Prob. 1CQ Ch. 9 - Prob. 2CQ Ch. 9 - Two pucks, of mass m and 4m, lie on a frictionless...Ch. 9 - Prob. 4CQ Ch. 9 - Prob. 5CQ Ch. 9 - Prob. 6CQ Ch. 9 - Prob. 7CQ Ch. 9 - Two students stand at rest, facing each other on...Ch. 9 - A 2 kg cart rolling to the right at 3 m/s runs...Ch. 9 - Automobiles are designed with crumple zones...

Ch. 9 - You probably know that it feels better to catch a...Ch. 9 - In the early days of rocketry, some people claimed...Ch. 9 - Two ice skaters, Megan and Jason, push off from...Ch. 9 - Suppose a rubber ball and a steel ball collide....Ch. 9 - While standing still on a basketball court, you...Ch. 9 - To win a prize at the county fair, youre trying to...Ch. 9 - Monica stands at the edge of a circular platform...Ch. 9 - If the earth warms significantly, the polar ice...Ch. 9 - Prob. 21CQ Ch. 9 - Prob. 23MCQ Ch. 9 - Curling is a sport played with 20 kg stones that...Ch. 9 - Prob. 25MCQ Ch. 9 - Prob. 26MCQ Ch. 9 - Prob. 27MCQ Ch. 9 - A 4.0-m-diameter playground merry-go-round, with a...Ch. 9 - A disk rotates freely on a vertical axis with an...Ch. 9 - At what speed do a bicycle and its rider, with a...Ch. 9 - Prob. 2P Ch. 9 - A 57 g tennis ball is served at 45 m/s. If the...Ch. 9 - Prob. 4P Ch. 9 - A student throws a 120 g snowball at 7.5 m/s at...Ch. 9 - Prob. 6P Ch. 9 - Prob. 7P Ch. 9 - Prob. 8P Ch. 9 - Use the impulse-momentum theorem to find how long...Ch. 9 - Prob. 10P Ch. 9 - Prob. 11P Ch. 9 - Prob. 12P Ch. 9 - A child is sliding on a sled at 1.5 m/s to the...Ch. 9 - Prob. 14P Ch. 9 - As part of a safety investigation, two 1400 kg...Ch. 9 - In a Little League baseball game, the 145 g ball...Ch. 9 - Prob. 18P Ch. 9 - A small, 100 g cart is moving at 1.20 m/s on a...Ch. 9 - Prob. 20P Ch. 9 - A 2.7 kg block of wood sits on a frictionless...Ch. 9 - Prob. 22P Ch. 9 - A 10,000 kg railroad car is rolling at 2.00 m/s...Ch. 9 - Prob. 24P Ch. 9 - A 55 kg hunter, standing on frictionless ice,...Ch. 9 - Prob. 26P Ch. 9 - Prob. 27P Ch. 9 - Prob. 28P Ch. 9 - A 71 kg baseball player jumps straight up to catch...Ch. 9 - Prob. 30P Ch. 9 - A kid at the junior high cafeteria wants to propel...Ch. 9 - The parking brake on a 2000 kg Cadillac has...Ch. 9 - A 2.0 kg block slides along a frictionless surface...Ch. 9 - Erica (36 kg) and Danny (47 kg) are bouncing on a...Ch. 9 - A 20 g ball of clay traveling east at 3.0 m/s...Ch. 9 - Prob. 37P Ch. 9 - A 20 g ball of clay traveling east at 2.0 m/s...Ch. 9 - A firecracker in a coconut blows the coconut into...Ch. 9 - Prob. 40P Ch. 9 - Prob. 41P Ch. 9 - Divers change their body position in midair while...Ch. 9 - Prob. 43P Ch. 9 - What is the angular momentum of the moon around...Ch. 9 - Prob. 46GP Ch. 9 - Prob. 47GP Ch. 9 - Prob. 48GP Ch. 9 - Prob. 49GP Ch. 9 - Prob. 50GP Ch. 9 - Prob. 51GP Ch. 9 - A 140 g baseball is moving horizontally to the...Ch. 9 - A tennis player swings her 1000 g racket with a...Ch. 9 - A 20 g ball of clay is thrown horizontally at 30...Ch. 9 - Dan is gliding on his skateboard at 4.0 m/s. He...Ch. 9 - Ethan, whose mass is 80 kg, stands at one end of a...Ch. 9 - Three identical train cars, coupled together, are...Ch. 9 - A 110 kg linebacker running at 2.0 m/s and an 82...Ch. 9 - Most geologists believe that the dinosaurs became...Ch. 9 - Two ice skaters, with masses of 75 kg and 55 kg,...Ch. 9 - Prob. 62GP Ch. 9 - One billiard ball is shot east at 2.00 m/s. A...Ch. 9 - A 10 g bullet is fired into a 10 kg wood block...Ch. 9 - A typical raindrop is much more massive than a...Ch. 9 - A 15 g bullet is fired at 610 m/s into a 4.0 kg...Ch. 9 - Prob. 67GP Ch. 9 - Two 500 g blocks of wood are 2.0 m apart on a...Ch. 9 - A spaceship of mass 2.0 106 kg is cruising at a...Ch. 9 - At the county fair, Chris throws a 0.15 kg...Ch. 9 - Prob. 73GP Ch. 9 - The carbon isotope 14C is used for carbon dating...Ch. 9 - Prob. 75GP Ch. 9 - A 2.0 kg, 20-cm-diameter turntable rotates at 100...Ch. 9 - Prob. 77GP Ch. 9 - A 3.0-m-diameter merry-go-round with a mass of 250...Ch. 9 - Disk A, with a mass of 2.0 kg and a radius of 40...Ch. 9 - Consider a golf club hitting a golf ball. To a...Ch. 9 - Consider a golf club hitting a golf ball. To a...Ch. 9 - Consider a golf club hitting a golf ball. To a...Ch. 9 - Consider a golf club hitting a golf ball. To a...

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