9. An arow is shot into the ajand moves along the paraboIic path y=X(50-X) (See figue). The horizontal component of veiocity is always 50 ft/s, What is the vertical COmPOnent Ofvelocitywhen (i) x= 10 and (ii) x=40? (i Calcuiate the derivative of y = X(50 - X) with respect to time. The vecomponent ofveloclty atX= 10 1S (SimpIify you answer.) (l ) The vertrd component ofveIoc-ty at X=40 1S (Simplify your answer.) S - S l / " S ) - ()(-()() "i' 1 2 ( S . S - / S / - !t-(-.-. 10"The hands ofa c10Ck in sometowerae appoximately 5 m and 2"5 m in length" Howfast is the distance between the tips Ofthe hands changing at 9:00? (Hint: Use the law of cosines.) Write an equation relating the angle between the two cIock hands, 0, and the distance between the tips ofthe two hands, C. Differentiate both sides of the equation with respect to t. The distance between the tips of the hands is changing at a rate of (Round to two decimaI p!aces as needed.) (1 m2/hr m3/h m/h .i) m 1 O/1 3/201 7Section 3.9-Oiiver Carver =. A !ighthouse stands 425 m off a straight shoe and the focused beam of its iight revoives four times each minute. As shown in the figue, P is the po On Shoe ciosestto the lighthouse and Q is a pojnt on the shoe 175 m fom P. What is the speed ofthe beam aiong the shoe whet stikes the point Q? Descibe how the speed ofthe beam along the shoe varies with the distance between P and Q. NegIect the height ofthe lighthouse. Q P ... 175ll Let x be the distance along the shore from point P to the beam and Iet O be the angIe through which the Iight evolves. Write an equation that reIates x and O, Derentiate both sides of the equation with espect to t. When the beam strikes the point Qts speed along the shore is about (Do not round unthe final answer. Then round to the nearest integer as needed.) How does the speed ofthe beam along the shoe vary with the distance between P and Q? A. The speed ofthe beam along the shoe is a constant because itdepends onIyon the distance fom the =ghthouse to P. B, lfQwee c10SertO Phen the speed ofthe beam along the shoe when it stike Q wouId be greater. C. IfQwere cIoseto P, then the speed ofthe beam aiong the shoe when it strike Q wouId be Iess. D. The speed ofthe beam along the shore is a constant because itdepends onlyon the rate at Which the Iight evolves. ) ) ( )