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HW7 - 3.X’m a,2 4 3 44,— 34 3>< C fl/Xx x...

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A-a W3 56E):'{ {(9% +Aw€+g omiz, 5(0): 0 —_, o: GHQ—ac: oa (SGE):~I<9+"+AJC) W VQE}: 0—» o:~3;d’+:4-—» JC air—W ' #WW‘ i-a 5-50 01 2’; “k ‘tzo 73) We 46(7):”392 FM/M’L—fi M: VH’F'MJC-Pc MA VCo): Ho fi./M.a \BZO+C,——§ C:((g—-7 Ivaréz—gz—buc, >~ W: 566): ~1e+1+re++c M 3(a):<g<~< —~> (9420+C—Q Qzéq—a 5%):“léfl—l— {62‘64—6q j a.) M : 569:0 —5 14%: +16% +¢q:o_, Math 16B Kouba Gravity Problems (The following problems ignore the effects of air friction and theoretical terminal velocities of falling objects). Begin each problem with the acceleration due to gravity of s”(t) = —32 ft. / sec2 . Then solve for instantaneous velocity 8’ (t) and height 8(t) 1.) Assume that the vertical motion of an object has initial velocity, em, and initial height, 80. Let 805) be the height (feet) of the object above the ground at time t (seconds). Begin with the acceleration due to gravity of ~32 ft /sec.2 and derive the height equation 805) = —16t2 + uot + 80 . 2.) A baseball is projected upward from the top of a 128-ft. high building at 112 ft / sec. a.) How high does the baseball go 7 b.) How long is the baseball in the air ? c.) What is the baseball’s velocity when t = 3 seconds ? t = 4 seconds? the ball strikes the ground ? 3.) A hard—boiled egg is projected downward from the top of a 320—ft. high building at 16 ft / sec. a.) In how many seconds will the egg strike the ground ? b.) What is the egg’s velocity when t = 1 second 7 t = 2 seconds? the egg strikes the ground ? 4.) An avocado is thrown upward from ground level and reaches its highest point in two seconds. a.) How high does the avocado go ? b.) What is the avocado’s initial velocity 7 5.) A rock falls from a 1600—ft. high cliff. a.) In how many seconds will the rock strike the ground ? b.) What is the rock’s velocity when t = 5 seconds ? the rock strikes the ground (in ft./sec. and miles/hr. where 1 mile 2 5280 ft.) ? 6.) A watermelon is thrown upward from ground level and reaches a maximum height of 144 feet. a.) How long does it take the watermelon to reach its highest point ? b.) How long is the watermelon in the air ? 1 c.) What is the watermelon’s initial velocity ? d.) What will happen to the watermelon when it strikes the ground 7 7.) A bowling ball falls from an airplane at an elevation of 8000 feet. a.) How long will it take the ball to reach an elevation of 1600 feet ? b.) What is the ball’s velocity at the elevation of 1600 feet ? 8.) A bottle of Snapple is thrown downward from a hovering helicopter from an unknown height and with an unknown initial velocity. The bottle falls from a height of 4000 feet to a height of 2400 feet in five (5) seconds and its velocity when t = 10 seconds is —400 ft. /sec. 9.) A water balloon is dropped from the top of a dormitory building. It strikes the ground in 5 seconds. a.) How high is the building ? b.) 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