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12–1. Abaseball is thrown downward from a 50-ft tower with an initial speed of 18ft>s.Determine the speed at which it hits the ground and the time of travel. SOLUTION v2 = v2 + 2a(s - s ) 2 1 c 2 1 v2 = (18)2 + 2(32.2)(50 - 0) 2 v = 59.532 = 59.5ft>s Ans. 2 v = v + a t 2 1 c 59.532 = 18 + 32.2(t) t = 1.29s Ans. This work is protected by United States copyright laws and is provided solely for the use of instructors in teaching their courses and assessing student learning. Dissemination or sale of any part of this work (including on the World Wide Web) will destroy the integrity of the work and is not permitted. © 2013 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This publication is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458. 12–2. When a train is traveling along a straight track at 2 m/s,it v s begins to accelerate at a = 160v-42m>s2,where visin m/s. Determine its velocity v and the position 3 s after the acceleration. SOLUTION dv a = dt dv dt = a 3 v dv dt = L L 60v-4 0 2 1 3 = (v5 - 32) 300 v = 3.925m>s = 3.93 m>s Ans. ads = vdv vdv 1 ds = = v5dv a 60 s 1 3.925 ds = v5dv L 60L 0 2 s = 1 av6b`3.925 60 6 2 = 9.98m Ans. This work is protected by United States copyright laws and is provided solely for the use of instructors in teaching their courses and assessing student learning. Dissemination or sale of any part of this work (including on the World Wide Web) will destroy the integrity of the work and is not permitted. © 2013 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This publication is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458. 12–3. From approximately what floor of a building must a car be dropped from an at-rest position so that it reaches a speed of 80.7 ft>s155mi>h2when it hits the ground? Each floor is 12 ft higher than the one below it.(Note:You may want to remember this when traveling 55mi>h.) SOLUTION (+T) v2 = v20 + 2ac(s - s0) 80.72 = 0 + 2(32.2)(s - 0) s = 101.13 ft 101.13 #of floors = = 8.43 12 The car must be dropped from the 9th floor. Ans. or laws teaching Web) in copyright Wide Dissemination permitted. States World instructors not of the is learning. United use on and by the for student work (including the protected solely of is work assessing this work and of integrity provided This is part the and courses any of destroy their will sale © 2013 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This publication is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458. *12–4. Traveling with an initial speed of 70km>h,a car accelerates at6000 km>h2along a straight road.How long will it take to reach a speed of 120 km>h? Also, through what distance does the car travel during this time? SOLUTION v = v + a t 1 c 120 = 70 + 6000(t) t = 8.33(10-3)hr = 30s Ans. v2 = v2 + 2a(s - s ) 1 c 1 (120)2 = 702 + 2(6000)(s - 0) s = 0.792km = 792 m Ans. or laws teaching Web) in copyright Wide Dissemination permitted. States World instructors not of the is learning. United use on and by the for student work (including the protected solely of is work assessing this work and of integrity provided This is part the and courses any of destroy their will sale © 2013 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This publication is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458. 12–5. A bus starts from rest with a constant acceleration of 1 m s2. > Determine the time required for it to attain a speed of 25 m s > and the distance traveled. SOLUTION Kinematics: v = 0,v = 25 m s,s = 0,and a = 1 m s2. 0 > 0 c > + A : B v = v0 + act 25 = 0 + (1)t t = 25 s Ans. + A : B v2 = v02 + 2ac(s - s0) or laws 252 = 0 + 2(1)(s - 0) teaching Web) in s = 312.5 m copyright Ans. Wide Dissemination permitted. States World instructors not of the is learning. United use on and by the for student work (including the protected solely of is work assessing this work and of integrity provided This is part the and courses any of destroy their will sale © 2013 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This publication is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458. 12–6. Astone A is dropped from rest down a well, and in 1 s another stone B is dropped from rest. Determine the distance between the stones another second later. SOLUTION 1 +T s = s + v t + a t2 1 1 2 c 1 s = 0 + 0 + (32.2)(2)2 A 2 s = 64.4ft A 1 s = 0 + 0 + (32.2)(1)2 A 2 s = 16.1ft B ¢s = 64.4 - 16.1 = 48.3ft Ans. or laws teaching Web) in copyright Wide Dissemination permitted. States World instructors not of the is learning. United use on and by the for student work (including the protected solely of is work assessing this work and of integrity provided This is part the and courses any of destroy their will sale © 2013 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This publication is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458. 12–7. A bicyclist starts from rest and after traveling along a straight path a distance of 20 m reaches a speed of 30 km/h. Determine his acceleration if it is constant.Also,how long does it take to reach the speed of 30 km/h? SOLUTION v = 30km>h = 8.33 m>s 2 v22 = v21 + 2ac(s2 - s1) (8.33)2 = 0 + 2ac(20 - 0) ac = 1.74m>s2 Ans. v = v + a t 2 1 c 8.33 = 0 + 1.74(t) t = 4.80 s Ans. or laws teaching Web) in copyright Wide Dissemination permitted. States World instructors not of the is learning. United use on and by the for student work (including the protected solely of is work assessing this work and of integrity provided This is part the and courses any of destroy their will sale © 2013 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This publication is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458. *■ 12–8. Aparticle moves along a straight line with an acceleration of a = 5>(3s1>3 + s5>2) m>s2, where s is in meters. Determine the particle’s velocity when s = 2m,if it starts from rest when s = 1m.Use Simpson’s rule to evaluate the integral. SOLUTION 5 a = A3s13 + s52B ads = vdv 2 5ds v = vdv L1 A3s13 + s52B L0 1 0.8351 = v2 2 v = 1.29m>s Ans. or laws teaching Web) in copyright Wide Dissemination permitted. States World instructors not of the is learning. United use on and by the for student work (including the protected solely of is work assessing this work and of integrity provided This is part the and courses any of destroy their will sale © 2013 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This publication is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458. 12–9. If it takes 3 s for a ball to strike the ground when it is released from rest, determine the height in meters of the building from which it was released.Also,what is the velocity of the ball when it strikes the ground? SOLUTION Kinematics: v = 0, a = g = 9.81 m s2, t = 3 s, and s = h. 0 c > +T v = v + at A B 0 c = 0 + (9.81)(3) = 29.4 m s Ans. > 1 +T s = s + v t + at2 A B 0 0 2 c 1 h = 0 + 0 + (9.81)(32) 2 or = 44.1 m Alaws ns. teaching Web) in copyright Wide Dissemination permitted. States World instructors not of the is learning. United use on and by the for student work (including the protected solely of is work assessing this work and of integrity provided This is part the and courses any of destroy their will sale © 2013 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This publication is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458.