Explanation Given information: The mass ( m ) of shell is 6 kg . The mass of fragment A is 3 kg . The mass of B fragment is 2 kg . The mass of C fragment is 1 kg . The velocity ( v 0 ) of shell is ( 12 m / s ) i − ( 9 m / s ) j − ( 360 m / s ) k Calculation: Refer from Figure P14.24 in the textbook. Express the position vector of A as follows: r A = − 1.5 i Express the position vector of B as follows: r B = 4 i + 2j Express the position vector of C as: r C = − 3 j Express the position vector of A / D as follows: r A / D = − 1.5 i − 4k r A / D = 1.5 2 + 4 2 = 18.25 = 4.272 Express the position vector of B / D as follows: r B / D = 4 i + 2j − 4 k r B / D = 4 2 + 2 − ( 4 ) 2 = 16 + 4 + 16 = 6 Express the position vector of C / D as follows: r C / D = − 3 j − 4k r C / D = ( − 3 ) 2 − ( 4 ) 2 = 9 + 16 = 5 Find the unit vector along ( λ A ) using the relation as follows: λ A = 1 r A / D ( r A / D ) (1) Substitute 4.272 for r A / D and − 1.5 i − 4 k for r A / D in Equation (1). λ A = 1 4.272 ( − 1.5 i − 4 k ) Find the unit vector along ( λ B ) using the relation as follows: λ B = 1 r B / D ( r B / D ) (2) Substitute 6 for r B / D and 4 i + 2j − 4 k for r B / D in Equation (2). λ B = 1 6 ( 4 i + 2j − 4 k ) Find the unit vector along ( λ C ) using the relation as follows: λ C = 1 r C / D ( r C / D ) (3) Substitute 5 for r C / D and − 3 j − 4 k for r C / D in Equation (3). λ C = 1 5 ( − 3 j − 4 k ) Consider that the change in the elevation due to gravity is neglected. Then, the velocity vectors after the explosion have the unit vector direction

Vector Mechanics for Engineers: Statics and Dynamics

12th Edition

ISBN: 9781259638091

Author: Ferdinand P. Beer, E. Russell Johnston Jr., David Mazurek, Phillip J. Cornwell, Brian Self

Publisher: McGraw-Hill Education

See similar textbooks

Concept explainers

Conservation of Energy

In physics, the rule of the conservation of energy states that energy doesn’t disappear from the atmosphere; instead, it changes its form from one type to another. Energy is one of the most important physical quantities in nature, and it cannot be create…

Videos

Question

Chapter 14.1, Problem 14.24P

To determine

Find the speed of each fragment A, B and C after the explosion.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 14.1, Problem 14.23P

Chapter 14.1, Problem 14.25P

Students have asked these similar questions

A 13-kg projectile is passing through the origin O with a velocity v0 = (35 m/s)i when it explodes into two fragments A and B , of mass 5 kg and 8 kg, respectively. Knowing that 3 s later the position of fragment A is (90 m, 7 m, -14 m), determine the position of fragment B at the same instant. Assume ay =-g= -9.81 m/s2 and neglect air resistance.

A 300-kg space vehicle traveling with a velocity v0 = (360 m/s)ipasses through the origin O at t = 0. Explosive charges then separate the vehicle into three parts A, B, and C , with mass, respectively, 150 kg, 100 kg, and 50 kg. Knowing that at t = 4 s, the positions of parts A and B are observed to be A (1170 m, -290 m, –585 m) and B (1975 m, 365 m, 800 m), determine the corresponding position of part C . Neglect the effect of gravity.

3. Neglecting air resistance, determine the value of the firing angle a in degree. At a horizontal distance of 12,000 ft, a projectile is fired with an initial velocity of 14.63 km/min at a target B located 6,096 decimeter above the gun A.

Chapter 14 Solutions

Vector Mechanics for Engineers: Statics and Dynamics

Ch. 14.1 - A 30-g bullet is fired with a horizontal velocity...Ch. 14.1 - Two identical 1350-kg automobiles A and B are at...Ch. 14.1 - An airline employee tosses two suitcases in rapid...Ch. 14.1 - Car A weighing 4000 lb and car B weighing 3700 lb...Ch. 14.1 - Two swimmers A and B, of weight 190 lb and 125 lb,...Ch. 14.1 - A 180-lb man and a 120-lb woman stand side by side...Ch. 14.1 - A 40-Mg boxcar A is moving in a railroad...Ch. 14.1 - Two identical cars A and B are at rest on a...Ch. 14.1 - A 20-kg base satellite deploys three...Ch. 14.1 - For the satellite system of Prob. 14.9, assuming...

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.

Find the speed of each fragment A , B and C after the explosion.

Solution Summary: The author calculates the speed of each fragment A, B, and C after the explosion.

Concept explainers

Videos

Find the speed of each fragment A, B and C after the explosion.

Want to see the full answer?

Chapter 14 Solutions