a. Answer s ' ( t ) = d s / d t = 64 − 32 t . s 2 ( t ) = d 2 s / d 2 t = − 32. s n ( t ) = − 32. Explanation Given information: On Earth, if you shoot a paper clip 64 ft straight up into the air with. a rubber band , the paper clip will be s ( t ) = 64 t − 16 t 2 feet above your hand at t sec after firing. Calculation: s ( t ) = 64 t − 16 t 2 . s ' ( t ) = d s / d t = 64 − 32 t . s 2 ( t ) = d 2 s / d 2 t = − 32. s n ( t ) = − 32. b. To determine To find: The time taken by the paper clip to reach its maximum height. Answer Maximum height reached at t = 2 second . Explanation Given information: On Earth, if you shoot a paper clip 64 ft straight up into the air with. a rubber band , the paper clip will be s ( t ) = 64 t − 16 t 2 feet above your hand at t sec after firing. Calculation: Set the first derivative equal to 0 and solve for t; because s(t) is a parabola with a negative sign, it will have one maximum and no minimum s ( t ) = 64 t − 16 t 2 . s ' ( t ) = d s / d t = 64 − 32 t = 0. 32 t = 64. t = 2 Maximum height reached at t = 2 second . c. To determine To find: The velocity at time t=0 is 64 ft/sec. Answer The velocity at time t=0 is 64 ft/sec. Explanation Given information: On Earth, if you shoot a paper clip 64 ft straight up into the air with. a rubber band , the paper clip will be s ( t ) = 64 t − 16 t 2 feet above your hand at t sec after firing. Calculation: Solve the first derivative at t=0 s ( t ) = 64 t − 16 t 2 . s ' ( t ) = d s / d t = 64 − 32 t . s ' ( 0 ) = 64 − 32 × 0 = 64. The velocity at time t=0 is 64 ft/sec. d. To determine To find: The maximum height. Answer Maximum height of 394.34 feet at t=12.3 second. Explanation Given information: On Earth, if you shoot a paper clip 64 ft straight up into the air with. a rubber band , the paper clip will be s ( t ) = 64 t − 16 t 2 feet above your hand at t sec after firing. Calculation: s ( t ) is an upside down parabola; it has one maximum and no minimum. By setting the first derivative equal to 0 and solving for t, we find that the maximum is achieved at t =12.3 seconds. Plugging t=12.3 into s ( t ) gives 394.34 feet as the maximum height. s ( t ) = 64 t − 2.6 t 2 . s ' ( t ) = d s / d t = 64 − 5.2 t = 0. 5.2 t = 64. t = 12.3. s ( 12.3 ) = 64 ( 12.3 ) − 2.6 ( 12.3 ) 2 = 394.34. Maximum height of 394.34 feet at t=12.3 second.

Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy)

4th Edition

ISBN: 9780133178579

Author: Ross L. Finney

Publisher: PEARSON

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Question

Chapter 3, Problem 71RE

To determine

To find: ds/dt and d2s/dt2.

Expert Solution

Answer to Problem 71RE

s'(t)=ds/dt=64−32t.s2(t)=d2s/d2t=−32.sn(t)=−32.

Explanation of Solution

Given information: On Earth, if you shoot a paper clip 64 ft straight up into the air with.

a rubber band ,the paper clip will be s(t)=64t−16t2 feet above your hand at t sec after firing.

Calculation:

s(t)=64t−16t2.s'(t)=ds/dt=64−32t.s2(t)=d2s/d2t=−32.sn(t)=−32.

To determine

To find: The time taken by the paper clip to reach its maximum height.

Expert Solution

Answer to Problem 71RE

Maximum height reached at t=2 second.

Explanation of Solution

Given information: On Earth, if you shoot a paper clip 64 ft straight up into the air with.

a rubber band ,the paper clip will be s(t)=64t−16t2 feet above your hand at t sec after firing.

Calculation:

Set the first derivative equal to 0 and solve for t; because s(t) is a parabola with a negative sign, it will have one maximum and no minimum

s(t)=64t−16t2.s'(t)=ds/dt=64−32t=0.32t=64.t=2

Maximum height reached at t=2 second.

To determine

To find: The velocity at time t=0 is 64 ft/sec.

Expert Solution

Answer to Problem 71RE

The velocity at time t=0 is 64 ft/sec.

Explanation of Solution

Given information: On Earth, if you shoot a paper clip 64 ft straight up into the air with.

a rubber band ,the paper clip will be s(t)=64t−16t2 feet above your hand at t sec after firing.

Calculation:

Solve the first derivative at t=0

s(t)=64t−16t2.s'(t)=ds/dt=64−32t.s'(0)=64−32×0=64.

The velocity at time t=0 is 64 ft/sec.

To determine

To find: The maximum height.

Expert Solution

Answer to Problem 71RE

Maximum height of 394.34 feet at t=12.3 second.

Explanation of Solution

Given information: On Earth, if you shoot a paper clip 64 ft straight up into the air with.

a rubber band ,the paper clip will be s(t)=64t−16t2 feet above your hand at t sec after firing.

Calculation:

s(t) is an upside down parabola; it has one maximum and no minimum. By setting the first derivative equal to 0 and solving for t, we find that the maximum is achieved at t =12.3 seconds. Plugging t=12.3 into s(t) gives 394.34 feet as the maximum height.

s(t)=64t−2.6t2.s'(t)=ds/dt=64−5.2t=0.5.2t=64.t=12.3.s(12.3)=64(12.3)−2.6(12.3)2=394.34.

Maximum height of 394.34 feet at t=12.3 second.

Chapter 3, Problem 70RE

Chapter 3, Problem 72RE

Chapter 3 Solutions

Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy)

Ch. 3.1 - Prob. 1QR Ch. 3.1 - Prob. 2QR Ch. 3.1 - Prob. 3QR Ch. 3.1 - Prob. 4QR Ch. 3.1 - Prob. 5QR Ch. 3.1 - Prob. 6QR Ch. 3.1 - Prob. 7QR Ch. 3.1 - Prob. 8QR Ch. 3.1 - Prob. 9QR Ch. 3.1 - Prob. 10QR

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Prob. 57RE Ch. 3 - Prob. 58RE Ch. 3 - Prob. 59RE Ch. 3 - Prob. 60RE Ch. 3 - Prob. 61RE Ch. 3 - Prob. 62RE Ch. 3 - Prob. 63RE Ch. 3 - Prob. 64RE Ch. 3 - Prob. 65RE Ch. 3 - Prob. 66RE Ch. 3 - Prob. 67RE Ch. 3 - Prob. 68RE Ch. 3 - Prob. 69RE Ch. 3 - Prob. 70RE Ch. 3 - Prob. 71RE Ch. 3 - Prob. 72RE Ch. 3 - Prob. 73RE Ch. 3 - Prob. 74RE Ch. 3 - Prob. 75RE Ch. 3 - Prob. 76RE Ch. 3 - Prob. 77RE Ch. 3 - Prob. 78RE Ch. 3 - Prob. 79RE Ch. 3 - Prob. 80RE Ch. 3 - Prob. 81RE Ch. 3 - Prob. 82RE Ch. 3 - Prob. 83RE

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d s / d t and d 2 s / d t 2 .

Videos

To find: ds/dt and d2s/dt2.

Answer to Problem 71RE

Explanation of Solution

To find: The time taken by the paper clip to reach its maximum height.

Answer to Problem 71RE

Explanation of Solution

To find: The velocity at time t=0 is 64 ft/sec.

Answer to Problem 71RE

Explanation of Solution

To find: The maximum height.

Answer to Problem 71RE

Explanation of Solution

Chapter 3 Solutions

Additional Math Textbook Solutions