Problem 94. \(\bullet \bullet\) A lemon is thrown straight up at \(15 \mathrm{~m} /\mathrm{s}\). (a) How much time does it take for the lemon to be \(5\mathrm{~m}\) above its release point? (b) How fast is the lemon moving when itis \(7 \mathrm{~m}\) above its release point? (c) How much time is required forthe lemon to reach a point that is \(7 \mathrm{~m}\) above its release point?Why are there two answers to part (c)? Ignore the effects of air resistance.Problem 95In the book and film Coraline, the title character and her new friend Wybiediscover a deep well. Coraline drops a rock into the well and hears the soundsof it hitting the bottom \(5.5 \mathrm{~s}\) later. If the speed of sound is\(340 \mathrm{~m} / \mathrm{s}\), determine the depth of the well. Ignore theeffects of air resistance.Problem 97\(\bullet \bullet\) A rocket is launched straight up. It contains two stages(Stage 1 and Stage 2) of solid rocket fuel that are designed to burn for\(10.0\) and \(5.0 \mathrm{~s}\), respectively, with no time interval betweenthem. In Stage 1, the rocket fuel provides an upward acceleration of \(15\mathrm{~m} / \mathrm{s}^{2}\). In Stage 2 , the acceleration is \(12\mathrm{~m} / \mathrm{s}^{2}\). Neglecting air resistance, calculate themaximum altitude above the surface of Earth of the payload and the timerequired for it to return back to the surface. SSMProblem 98•e• A lacrosse ball is hurled straight up, leaving the head of the stick at aheight of \(2.00 \mathrm{~m}\) above ground level. The ball passes by a\(1.25\)-m-high window in a time of \(0.4 \mathrm{~s}\) as it heads upward.Calculate the initial speed of the ball if it is \(13 \mathrm{~m}\) from theground to the bottom of the window. Ignore the effects of air resistance.Problem 99Biology A black mamba snake has a length of \(4.3\) \(\mathrm{m}\) and a top speedof \(8.9 \mathrm{~m} / \mathrm{s}\) ! Suppose a mongoose and a black mamba findthemselves nose to nose. In an effort to escape, the snake accelerates at \(18\mathrm{~m} / \mathrm{s}^{2}\) from rest. (a) How much time does it take forthe snake to reach its top speed? (b) How far does the snake travel in thattime? (c) Has the tail of the snake gone past the mongoose or does themongoose have a chance to catch the black mamba?Problem 100-Sports Kharissia wants to complete a \(1000-\mathrm{m}\) race along a straight road with an average speed of \(8 \mathrm{~m} / \mathrm{s}\). After \(750 \mathrm{~m}\), she has averaged \(7.2 \mathrm{~m} / \mathrm{s}\). What average speed must she maintain for the remainder of the race in order to attain her goal?Problem 101• Sports In April 1974 , Steve Prefontaine completed a \(10-\mathrm{km}\) racein a time of \(27 \mathrm{~min}, 43.6 \mathrm{~s}\). Suppose "Pre" was at the\(9-\mathrm{km}\) mark at a time of \(25 \mathrm{~min}\) even. If he acceleratesfor \(60 \mathrm{~s}\) and maintains the increased speed for the duration of therace, calculate the acceleration that he had. Assume his instantaneous speedat the \(9-\mathrm{km}\) mark was the same as his overall average speed at thattime.Problem 102•An egg is thrown straight down at \(1.5 \mathrm{~m} / \mathrm{s}\) from a talltower. Two seconds \((2\) s) later, a second egg is thrown straight up at \(4.0\mathrm{~m} / \mathrm{s}\). How far apart are the two eggs \(4 \mathrm{~s}\)after the second egg is thrown? What is the minimum separation between theeggs and when does it occur? Ignore the effects of air resistance.Problem 103•A two-stage rocket blasts off vertically from rest on a launchpad. During thefirst stage, which lasts for \(15.0 \mathrm{~s}\), the acceleration is aconstant \(2.00 \mathrm{~m} / \mathrm{s}^{2}\) upward. After \(15.0 \mathrm{~s}\),the first engine stops and the second stage engine fires, producing an upwardacceleration of \(3.00 \mathrm{~m} / \mathrm{s}^{2}\) that lasts for \(12.0\mathrm{~s}\). At the end of the second stage, the engines no longer fire andtherefore cause no acceleration, so the rocket coasts to its maximum altitude.(a) What is the maximum altitude of the rocket? (b) Over the time intervalfrom blastoff at the launchpad to the instant that the rocket falls back tothe launchpad, what are its (i) average speed and (ii) average velocity?Ignore the effects of air resistance.Problem 104Calc Air drag plays a significant role in the free fall of objects nearEarth's surface. Suppose the acceleration of a falling object is given by thefollowing function $$ a(v)=g-\alpha v \quad \text { (down is positive) } $$ where \(\alpha\) is a positive constant. (a) By integrating, find the velocityof a falling object as a function of time. (b) Find the terminal velocity ofan object that falls from rest starting at \(t=0\).
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