Download Quadratic Word Problems Worksheet 1. The Empire

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Quadratic Word Problems Worksheet
1. The Empire State Building is 1250 feet tall. If an, object is thrown upward from the top of the building
at an initial velocity of 38 feet per second, its height s seconds after it is thrown is given by the function
h(s) ::;: -168 2 + 388 + 1250. How long will it take for the ball to hit the ground?
2. A juggler throws a ball into the air, releasing it 5 feet above the ground with an initial velocity of
15 ftlsre. She catches the ball with her other hand when the ball returns to 5 feet above the ground. If the
equation h = -16/ 2 + 1St gives the path of the ball from hand to hand, find how long the ball is in the air.
3. A ball is thrown straight up with an initial velocity of 56 feet per second. The height, h, of the ball 1
seconds after it is thrown is given by the formula h(/) = 561 -161 2
a) What is the maximum height?
b) What is the height of the ball after 1 second? c) After how many seconds will it return to the ground? 4. A ball is thrown upward from the ground. Its height (h, in feet) is given by the function
h =-161 2 +641 +3, where t is ~e length of time (in seconds) that the ball has been in the air. What is the
maximum height that the ball reaches?
5. The height, h(t), in feet, of an object shot from a cannon with initial velocity of 20 feet per second can
be modeled by the equation h(/) =-16/ 2 + 201 + 6, where t is the time. in seconds. after the cannon is
fired. What is the maximum altitude that the object reaches?
6. Physicists tell us that altitude h in feet ofa projectile t seconds after firing is h =-16/ 2 + vat + ho •
where Vo i$ the initial velocity in feet per second and ho is the altitude in feet from which it is fired. If a
rocket is launched from a hilltop 2400 feet above the desert with an initial upward velocity of 400 feet per
second~ then when will it land on the desert?
7. The engine torquey (in foot-pounds) of one model ofcar is given by y = -3.75x 2 +23.23+38.8 where
x is the speed ofthe engine (in thousands ofrevolutions per minute).
a) .Find the engine speed that maximizes the torque. b) What is the maximum torque?
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8. In baseball, the flight ofa pop-up may be described as d =-16t 2 +80/+3.5 where d gives the ball's
height above the ground in feet as a function oftime I. How long does the catcher have to get into
position under the ball after the ball is hit?
9. When a gray kangaroo jumps, its path through the air can be modeled by y =-0.0267x2 +0.8x where
x is the kangaroots horizontal distance traveled (in feet) and y is its corresponding height (in'feet).
a) How high can a gray kangaroo jump?
.
b) How far can it jump?
Quadratic Word Problems Worksheet
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1. The Empire State Building is 1250 feet talL If an, object is thrown upward from the top of the building
at an initial velocity of38 feet per second, its height 8 seconds after it is thrown is given by the function
h(s):;: -168 2 +388+1250. How long will it take for the ball to hit the ground? .:X 10,) 5 ect'r?dS
2. A juggler throws a ball into the air, releasing it 5 feet above the ground with an initial velocity of . '< 15 ftJsec. She catches the ball with her other hand when the ball returns to 5 feet above the ground. If the '#."'\(\ equation h =-16/ 1 + 15t gives the path of the ball fr~rr. hand to h~<L find how lpng the ball is in th.e air.,
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3. A ball is thrown straight up with an initial velocity of56 feet per second. The height, h, ofthe ball 1 ~
seconds after it is thrown is given by the formula h{t) =56t -16t 2
~.I : Vt~ a) What is the maximum height? £;'1 -Fe~+(J . . 1 5} '1 f)
5Y.1)- .(.f(l· b) What is the height of the ball after 1 second? 'j 0 .(:-ee+ c) After how many seconds will it return to the ground? :, .. S 5 e.evn~ fit
Vert-ex
4. A ball is thrown upward from the groWld. Its height (h, in feet) is given by the function
h =-16t2 + 64t + 3, where t is !he length oftime.{in seconds) that the ball has been in the air. What is the
maximum height that the ball reac'hes?
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-r + h
5. The height, h(t), in feet, of an object shot from a cannon with initial velocity of20 feet per second can
be modeled by the equation h{t) =-16t' + 20t + 6, where t is the time, in seconds, after the cannon is
fired. What is the maximum altitude that the object rea~hes? f :;.
5 fee4- h \, ~h
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6. Physicists tell us that altitude h in feet of a projectile t seconds after firing is h = -16t 2 + Vol + he ,
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where Yo i$ the initial velocity in feet per second and ho is the altitude in feet from which it is fired. Ifa
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rocket is launched from a hilltop 2400 feet above the desert with an initial upward velocity of 400 feet per
second, the~i1l it land on the desert? h:::. -) t;, t 2.+ 4" 0 i:; +..l '1 Q'O
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7. The engine torque y (in foot-pounds) ofone model ofcar is given by y =-3.75x 2 + 23.4('+ 38.8 where x is the speed of the engine (in thousands of revolutions per minute). ~('y..t
a) Find the engine speed that maximizes the torque. M CA.:~ SreeJ. ~ ¥1Ifii!1 3..01 b) What is the maximum torque? VV'o.::.x Tc(''fl.(€.. 7'1,7
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8. In baseball, the flight of a pop-up may be described as d = -16t~ + 80t + 3.5 where d gives the ball's
'f.:"'\ (\') height above the ground in feet as a function of time t. How long does the catcher have to get into
'
position under the ball after the ball is hit? ~
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9. When a gray kangaroo jumps, its path through the air can be modeled by y == -O.0267x2 + 0.8x where
X is the kangaroo's horizontal distance-traveled (in feet) and y is its corresponding height (in feet). Ve..--le>, a) How high can a gray kangaroo jpmp? •.::0 S Viti!l\iij ;::l:::. G::. \ee\ . X-;I'\~ b) How far can itjump?:v2A" \ee\!i o.:;Jil ieC\ ~ :zq, Cj or 6() .f~&. ·
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