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Unformatted text preview: Math 17A Kouba ,,
Gravity Problems (The following problems ignore the effects of air friction and theoretical terminal velocities of falling objects). Assume that the height function is
8(t) 2' —16t2 + ’0013 + 80 , where so is the initial height and 110 is the initial velocity. 1.) 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 ? 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 ? 2.) 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 '3
b.) What is the egg’s velocity when i: = 1 second ? t = 2 seconds? the egg strikes the
ground ? 3.) An avocado is thrown upward from ground level and reaches its highest point in two
seconds. a.) How high does the avocado g0 ?
b.) What is the avocado’s initial velocity ? 4.) 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.) ? 5.) 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 I7 c.) What is the watermelon’s initial velocity ? d.) What will happen to the watermelon when it strikes the ground ? 6.) A bowling ball falls from an airplane at an elevation of 8000 feet. 1 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 7 7 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. ) What is the bottle’s initial velocity ? ) What is the bottle’s initial height ? How long is the bottle in the air ? d.) What is your favorite kind of Snapple drink ? a
c 8.) 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.) What is the balloon’s velocity after 1 second ? after 3 seconds ? c.) What is the balloon’s velocity as it strikes the ground (in ft. / sec) ? (in miles per
hour) ? ...
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- Winter '08