Chapter 3 76

# Chapter 3 76 - 226 30 We want to ﬁnd — when L = 31...

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 226 30. We want to ﬁnd — when L = 31. WearegiventhatZ—g: =2ft/s.sin0= {80 => \$210sin6 => d1: d6 71' 7r d9 — 2 1 6—. = —— = — — 10 dt Ocos dt When 6 4, 2 10 cos 4 dt => d6 2 \/§ x — : ———- = — rad/s dt 10(1/05) 5 . . i . dm , dy 32. P Usmg Q for the orlgin, we are given a = —2 ft / s and need to find E when m z —5. Using the Pythagorean Theorem twice, we have V322 + 122 + y2 + 122 = 39, the total length of the rope. Differentiating Q y _ x dz: y dy With res ecttot, we et ———— + ————— = 0, so p g «9:2 + 122 dt My? + 122 dt dy so My? —— 122 dm ——:f————————<PWWWMHm=#539:\/—52+1P%- 24422213+ 2+122 ¢> dt y GﬁfiTiii dt ( ) y x/y My? + 122 : 26, and y : V262 - 122 = V532. So when x = —5, dy : (—5)(26) ( 2) — ———10— m —0.87 ft/s. So cart B is moving towards Q at about 0.87 ft/s. dt 4/532(13) x/133 33. (a) By the Pythagorean Theorem. 40002 + y2 2 £2. Differentiating with respect 6 to t, we obtain 2y % = 23:17:. We know that 2—: : 600 ft/s, so when 4000 y : 3000 ft, 2 : \/ 40002 + 30002 : «25,000,000 : 5000 ft and d! y dy 3000 1800 - —-— 600 ————360ft dt 6 t 5000( ) 5 / 2 __y_ i _i_y_ ”ELLE : @26089‘11 (bIIIGBtan6“ 4000 dtaane)" dt(4000) Z? sec dt 4000 t dt 4000 dt dB _ dB dW dL E?_dW’ﬂ;ﬁ dB dt CHAPTER 3 DIFFERENTIATION RULES 18mmg3200mwﬂﬂmmw/20HL“? : (0.007. %W_1/3)(0.12 '2'53. L1.53)<_2_0_i> 10,000,000 5 = 01007.§(012.18253)‘“3]0112.253-18153)<——~) % L045><10_8g/yr 107 dy _‘ _ ﬂ _ : When y — 3000 ft‘ E — 600 ft/s. E — 5000 and 0050 ! —_Z # #5000 99 dt “/32 4000 4000 4000 :1 5 (600) 2 0.096 rad/s. ...
View Full Document

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern