i6c*mzr \O+hf tlnu s\ock- L Quadratic Racl't cz ae! #- Formula Word Problems Name: Period: 1. Jason jumped off of a cliff into the ocean in Acapulco while vacationing with some friends. His height as a function of time could be modeled by the function h(t) = -16t2 +l6t + 480, where t is the time in seconds and h is the height in feet. a. How long did it take for Jason to reach his maximum height? b. What was the highest point that Jason reached? c. Jason hit the water after how many seconds? 2. ll atoy rocket is launched vertically upward from ground level with an initial velocity of 128 feet per \- second, then its height h after f seconds is given by the equation h(t1 = -t6t2 +128t (if air resistance is neglected) a. How long will it take for the rocket to return to the ground? b. After how many seconds will the rocket be 112 feet above the ground? c. How long will it take the rocket to hit its maximum height? d. What is the maximum height?
3. A rocket is laurfched from atop a 101 - foot cliff with an initial velocity of 1 16 fus. a. Substitute the values into the vertical motion formula h(t1= -l6tz +vt +ho. Let h(t) = O b. Use the quadratic formula to find out how long the rocket will take to hit the ground after it is launched. Round to the nearest tenth of a second. \./ 4. You and a friend are hiking in the mountains. You want to climb to a ledge that is 20 ft. above you. The height of the grappling hook you throw is given by the function h(t1= -l6tz -32r +5. What is the maximum height of the grappling hook? Can you throw it high enough to reach the ledge? 5. You are trying to dunk a basketball. You need to jump 2.5 ft. in the air to dunk the ball. The height that your feet are above the ground is given by the function h(t) = -76t2 +I2t. What is the maximum height your feet will be above the ground? Will you be able to dunk the basketball? 6. A diver is standing on a platform 24 ft. above the pool. He jumps filrm the platform with an initi8al upward velocity of 8 fus. Use the lormulah(t) = -16t2 +vt + s, where h is his height above the water, t is the time, v is his starting upward velocity, and s is his starting height. How long will it take for him to hit the water? 7. A ball is thrown upward from a height of 15 ft. with an initial upward velocity of 5 fvs. Use the formula h(t) = -16t2 +vt + s to find how long it will take for the ball to hit the ground.
8. n trebuchet lagnches a projectile on a parabolic arc at a velocity of 35 fvs. Using the function h(t)=-l6t+vt*h, determine when the projectile willfirst reach a height of 80 ft., and how many. seconds later will it again be 80 feet. L '1. During World War I, mortars were fired from trenches 3 feet down. The mortars had a velocity of 150 ftls. Determine how long it will take for the mortar shell to strike its target. i1). One of the games at a carnival involves trying to ring a bell with a ball by hitting a lever that propelstheball intotheair. Theheightoftheball ismodeledbytheequation h(t1=-16t2+39r. lfthe bell is 25 ft. above the ground, will it be hit by the ball? [1. A ship drops anchor in a harbor. The dnchor is 49 ft. above the surface of the water when it is released. Use the vertical motion formula h = -!6tz +vt + s to answer the following questions. a. What is the value of x, the starting height? b. What is the value of h when the anchor hits the water? c. The starting velocity is zero. After how many seconds willthe anchor hit the water? l1: nn amateur rocketry club is holding a competition. There is cloud cover at 1000 ft. lf a rocket is launched with a velocity of 31 5 fvs, use the f unctio n h@ = -l6t + vt +ho io determine how long the rocket is out of sight.
qr*ober \O+h+ tlnk B\ock-,/'(?vclc}.tce!"+ +.-. Quadratic Formula Word Problems t\ \./ 1. Jason jumped off of a cliff into the ocean in Acapulco while vacationing with some friends. His height as a function of time could be modeled by the function h(t) = -l6tz +l6t + 480, where t is the time in seconds and h is the height in feet. a. How long did it take for Jason to reach his tnaxi -lr, -j2- b. What was the highest point that Jason reached? htt) =\K cl 4tu urn_beight? c. Jason hit the water after how many seconds? -ta!jffiu -32-5 a.-...--...-...-.'...--...-- 2. lf a toy rocket is launched vertically upwardl6m ground level with an initial velocity of 128 feet per \- second, then its height h after f seconds is given by the equation h(t1 = -76t2 +L28t (if air resistance is a. How long will it take for the rocket to return to the ground? o =-bf+tzg+ -tb+ (t -r) -V- - T / _% g Se-ro4J5 b. After how many seconds will the rocket be 1 12 feet above ll1- = -rcokz+\zy+ o= -tr*+vg+-tll O = -tb (t-t+ +-l) = -tulk c. How long will it take the rocket to hit its maximum height? d. What is the maximum height? \ aacpnls I szufitd, on hrory vt +,tt*s oa+ wqr
q.b) A rocket is launched from atop a 101 - foot cliff with an initial velocity of 116 fvs. a. substitute the values into i66vertical motion formula h(t1 = -iffi h- Let h(t) = o P. Ul. the quadratic formula to find out how long the rocket will take to hit the ground after launched. Round to the nearest tenth of a second. h Lu) = 4bt + \ltot + to \ Ab* (,ot'{ sacord-s -n?- 4. You and a friend are hiking in the mountains. You want to climb to a ledge that is 20 ft. above you. The height of the grappling hook you throw is given by the function he) = -!6tz -32t +5. what is the maximum height of the grappling hook? Can you throw it high enough to reach the ledge? ) 2b- -=3?- -7> _ -l h(-,\ = Zt Th,u mhv 1o w.( he,<h+ o,,,ft \ z L lyu ab\c p6tl, n7 +. ftost is et $dl rearl /l,u- lllk" 5' You are trying to dunk a basketball. You need to ju[p_zslun the air to dunk the bal]. The hgfihi that your feet are above the ground is given by the funciioffiil t6t2 +12t. Whatis the maximum h"ight yorr f""t *ilt b" nd? wiu you be able to finrlhe oask6tuattz _b?tr = 7.zS m^y hey[tl is 2,ZS no J.,,n UnJ Q" ^<. 6' A diver is standing on a platform24 ft. above the pool. He jumps fbrm the platform with an initisal upward velocity of 8 fus. Use the formulah(t) = -16t2 +vt +s, where h is his height above the water, t is the time, v is his starting upward velocity, and s is his starting height. How long will it take for him to hit the water? f;., 4 hru\ = -ltftln gl+ zq -ql - -g!4o * =Q,715-7?- h to,?" s) _7L 7. A ball is thrown upward from a height of 1S'ft. with an initial upward velocitv of 5 fvs. Use the formula h(t1 = -l6tz +vt +s to findffi tong it will take for the uatt to hitlg?:--...- -- hr&)= -tb*+b#+ts &borl- \ 'l7n 5Lto FIS ea\42- Q= -lbtz+}t,+ l(- r,5 [,5 >elonj_s
I. LHP&IfaQnches a projectile on.a parabolic arc at a velocity of 35 fus. Using the function h(t) = -16i"+vt + h, determine when the ilrojectile will first reach a height of g0 ft., and how many seconds later will it again be 80 feet. h&)= -t6-&+3bl = -ll<?+"=<+ -lt'*+7f{-8o fievo( k*thts g0?+ thc h,r I'qtl-.'Y'-@, i5@ 150fUs.DeterminehowIongitwilltakefortheffi hctl= -tt,&+\50+ -3 0 = -lbtz+ l;ot -3,/o P^o I?,JW rs had a velocity of + = -21 lwa1,ttl -3>-- ifl. One of the games at a carnival involves trying to ring a bell with a ball by hitting_a lever that propelstheball intotheair. Theheightoftheball ismodeledbytheequation hg)=-t6t?+39r. lfthe bell is 25 ft. above the ground, will it be hit by the ball? Z5 = -ltl,lyn+ L = -vll ri;1-3?- U. A ship drops anchor in a harbor. The dnchor is 49 ft. above the surface of the water when it is released. UGTne-vertical mo to answer the following questions. a. What is the e rrrvltvtt rr.ttttffi,, - b. What is the value of h when k).7 -tuf-rh g * tl,?s l r*j ^F; f.z{tl *^nd; nlo +,^r,\l ^,rl fzuh Zq C+ Z<*d' -$^c h<-t1hl -- O hrtth;f --O. c. The starting velocity is zero. After how many seconds will the anchor hit the water? r,tt\c-n k{+"r 1,75 aetonj I ooo l1: nn amateur rocketry club is holding a competition. There is cloud cover at 1000 ft. If a rocket is launched with a velocity of 315 fvs, use the function h(t) = -t6hvt * hoto determine how long the rocket is out of sight. h(t) = -lbtz {r "\6 t -l b&3\5+ tooo = O > 4tot?.+E\6L -;CI o c/ t)s.z t - 3,1 I