Math 104 _ q2v0v1m6b `Kau`thaq ]SPoEfOtHwOaCrmeC rlsljc^.s f UAOlAlO NrUihgohatOst iree`see]rkveebdr. Motion Projectile Problems (MPP) 30102016 1) Erika jumped off a cliff into the ocean in Acapulco while vacationing with some friends. Her height as a function of time could be modeled by the function h(t) = -16t 2 + 16t + 96 where t is the time in seconds and h is the height in feet. 2) If a toy rocket is launched vertically upward from ground level with an initial velocity of 128 feet per second, the its height h after t seconds is given by the equation h(t) = -16t 2 + 128t (if air resistance is neglected). a) How long did it take Erika to reach her b) What was the highest point that Erika reached? c) After how many seconds did Erika hit the a) How long will it take the rocket to return to the b) After how many seconds will the rocket be 112 feet above the c) How long will it take the rocket to hit its d) What is the 3) You are trying to dunk a basketball. You need to jump 2.5 feet in the air to dunk the basketball. The height that your feet are above the ground is given by the function h(t) = -16t 2 + 12t. What is the maximum height your feet will be above the Will you be able to dunk the basketball? 4) Cyndie is standing on a platform 24 feet above the pool. She jumps from the platform with an initial upward velocity of 8 feet per second. Her height after t seconds is given by the function h(t) = -16t 2 + 8t + 24. a) What is her maximum height above the b) How long does it take her to reach the c) How long will it take her to hit the 5) Dash and Ron are hiking in the mountains. They want to climb to a ledge that is 20 feet above them. The height of the grappling hook they throw is given by the function h(t) = -16t 2 + 32t + 5. a) Is it possible to throw the grappling hook so it will catch on the ledge and allow them to reach the ledge? b) What is the maximum height of the grappling hook? 6) A ball is thrown directly upward from an initial height of 200 feet with an initial velocity of 96 feet per second. The height of the ball thrown is given by the function h(t) = -16t 2 + 96t + 200. 100 feet above the N G2I0I1w6d HKZuQtbak NSGosfKtnwmafrxe] eltlgco.] q \AslslC `rcizgphvtksx Kr]eCsLe^rPv`eTdt.] t ]MkahdseM zwaiktwhb NIfnUfBiensistdeI `APlHgte^bPrfaF \2J. -1-
7) Some fireworks are fired vertically into the air from the ground at an initial velocity of 80 feet per second. The path of a firework is modeled by h(t) = -16t 2 + 80t. a) How long does it take for the firework to d) How long will it take for the firework to be 100 feet above the 8) A ball is thrown vertically upward with an initial velocity of 48 feet per second. If the ball started from a height of 8 feet off the ground. The path of the ball is modeled by h(t) = -16t 2 + 48t + 8. 56 feet above the 9) A pistol is accidentally discharged vertically upward at a height of 3 feet above the ground. If the bullet has an initial muzzle velocity of 200 feet per second. The path of the bullet is modeled by h(t) = -16t 2 + 200t + 3. a) How long does it take for the bullet to d) When will the bullet be 403 feet above the 10) An over zealous golfer hits a flop shot with a sand wedge to get out of the corner of a sand trip with an initial velocity of 45 feet per second.the path of the golf ball is modeled by h(t) = -16t 2 + 45t. a) How long does it take for the golf ball to d) When will the golf ball be 10 feet above the 11) Abigail tosses a coin off a bridge into the stream below. The distance, in feet, the coin is above the water is modeled by equation h(t) = -16t 2 + 96t + 112. a) How long does it take for the coin to d) When will the coin be 30 feet above the 12) At a swim meet, Janet dives from a diving board that is 48 feet high. Her position above the water is represented by the equation h(t) = -16t 2 + 24t + 48. where t represents time in seconds and h(t) represents height in feet. a) After how many seconds does Janet enter the b) What is the greatest height Janet reaches in her dive? c) How long will it take to reach the max height? z T2W0u1`6p okmu_tras zsaojfutnwua^rrec mltlacb.f n `Aelclo QroiggwhotYst MrYeesKeprJvNejdP.f N pmxandseh cwsiwt_hm RI_nVfGiWnsiZtie_ ma]lhgqeubtrkag k2m. -2-
13) American astronauts working on a space station on the moon toss a ball into the air. The height of the ball is represented by the equation h(t) = -2.7t 2 + 13.5t + 14, where t represents time in seconds since the ball was thrown and f(t) represents the height of the ball in feet. 14) Jenn and Chelsea built rockets from assembly kits and are going to launch them at the same time to see whose rocket flies higher. If Jenn's rocket's height, in feet, can be described by the equation J(t) = -16t 2 + 180t, while Chelsea's is represented by C(t) = -16t 2 + 240t. a) After how much time does the ball hit the Round to the nearest tenth. b) what is the greatest height the ball achieves? Round to the nearest tenth. a) Who wins the rocket race? (What is the max height for both rockets?) b) After how many seconds does each rocket land? c) To the nearest tenth of a second, what was the difference in time for the two different rockets to reach their respective max heights? G o2o0y1q6g QKluXtWai gsfo`fythwjayryes ILNLOCo.p S \ADlklr srsicgdhgtcsg friecscefrivmeyd^.m d amtasdweb LwCiTtchR OIonhfPiAnTiqtRet taxlrgyebbiryae C2r. -3-
Math 104 L m2a0h1f6y ekguitfaw ysvojfotkw\ayrbe] alyl[cy.q Z fadlwlo croiqgqhetssa xrpezsme`ravieadm. Motion Projectile Problems (MPP) 30102016 1) Erika jumped off a cliff into the ocean in Acapulco while vacationing with some friends. Her height as a function of time could be modeled by the function h(t) = -16t 2 + 16t + 96 where t is the time in seconds and h is the height in feet. a) How long did it take Erika to reach her b) What was the highest point that Erika reached? c) After how many seconds did Erika hit the 3) You are trying to dunk a basketball. You need to jump 2.5 feet in the air to dunk the basketball. The height that your feet are above the ground is given by the function h(t) = -16t 2 + 12t. What is the maximum height your feet will be above the Will you be able to dunk the basketball? a) 1 second 2) If b) a toy 100 rocket feet c) is 3 launched seconds vertically 2 upward from ground level with an initial velocity of 128 feet per second, the its height h after t seconds is given by the equation h(t) = -16t 2 + 128t (if air resistance is neglected). a) How long will it take the rocket to return to the b) After how many seconds will the rocket be 112 feet above the c) How long will it take the rocket to hit its d) What is the a) 8 seconds b) at 1 and 7 seconds c) 4 seconds d) 25 a) 4 1 feet 4) Yes Cyndie is standing on a platform 24 feet 2 above the pool. She jumps from the platform with an initial upward velocity of 8 feet per second. Her height after t seconds is given by the function h(t) = -16t 2 + 8t + 24. a) 25 feet a) What is her maximum height above the b) How long does it take her to reach the c) How long will it take her to hit the 5) Dash and Ron are hiking in the mountains. They want to climb to a ledge that is 20 feet above them. The height of the grappling hook they throw is given by the function h(t) = -16t 2 + 32t + 5. a) Is it possible to throw the grappling hook so it will catch on the ledge and allow them to reach the ledge? b) What is the maximum height of the grappling hook? a) yes b) 21 feet 6) A ball is thrown directly upward from an initial height of 200 feet with an initial velocity of 96 feet per second. The height of the ball thrown is given by the function h(t) = -16t 2 + 96t + 200. 100 feet above the a) 3 seconds b) 344 feet c) approximately 7.6 seco I A2I0x1s6K BKEu\t_aW MSZojfZtKwNadrpeO _LSLXCO.^ K ]AelilD Br^iEgahMt]sM rrxe`sfexrnvmezdr.k l gmhaad_er JwNivthhs yi_nhfyihniibtseb vahlsgteabdroaa S2K. -1-
7) Some fireworks are fired vertically into the air from the ground at an initial velocity of 80 feet per second. The path of a firework is modeled by h(t) = -16t 2 + 80t. a) 2 1 2 seconds 8) A ball b) is thrown 200 feet vertically c) 5 seconds upward with an initial velocity of 48 feet per second. If the ball started from a height of 8 feet off the ground. The path of the ball is modeled by h(t) = -16t 2 + 48t + 8. a) 1 1 2 secon 50 feet, sin a) How long does it take for the firework to d) How long will it take for the firework to be 100 feet above the 56 feet above the 9) A pistol is accidentally discharged vertically upward at a height of 3 feet above the ground. If the bullet has an initial muzzle velocity of 200 feet per second. The path of the bullet is modeled by h(t) = -16t 2 + 200t + 3. a) How long does it take for the bullet to d) When will the bullet be 403 feet above the a) 6 1 seconds 10) An over b) 628 zealous feet golfer c) approximately hits a flop shot 12.5 with seconds a) 1 13 d) A 4 a sand wedge to get out of the corner of a 32 se seconds and sand approximately trip with an 1.4 initial seconds. velocity of 45 feet per second.the path of the golf ball is modeled by h(t) = -16t 2 + 45t. a) How long does it take for the golf ball to d) When will the golf ball be 10 feet above the 11) Abigail tosses a coin off a bridge into the stream below. The distance, in feet, the coin is above the water is modeled by equation h(t) = -16t 2 + 96t + 112. a) How long does it take for the coin to d) When will the coin be 30 feet above the 12) At a swim meet, Janet dives from a diving board that is 48 feet high. Her position above the water is represented by the equation h(t) = -16t 2 + 24t + 48. where t represents time in seconds and h(t) represents height in feet. a) After how many seconds does Janet enter the b) What is the greatest height Janet reaches in her dive? a) 3 seconds b) 256 feet c) 7 seconds d) approximately c) How 5.0 long seconds. will it take to reach the max height? a) approx I E2y0y1A6] CKAuWtNam hsyowfjt`wxa[roej llolycp.e o gahlxlf [rti`gchstdsf iryens[ejrqvxe_dq.` J WMaahdUe] ]wyiztth\ QIznCf_ivnEiOtbeW raxldgvecbersaa G2F. -2-
13) American astronauts working on a space station on the moon toss a ball into the air. The height of the ball is represented by the equation h(t) = -2.7t 2 + 13.5t + 14, where t represents time in seconds since the ball was thrown and f(t) represents the height of the ball in feet. 14) Jenn and Chelsea built rockets from assembly kits and are going to launch them at the same time to see whose rocket flies higher. If Jenn's rocket's height, in feet, can be described by the equation J(t) = -16t 2 + 180t, while Chelsea's is represented by C(t) = -16t 2 + 240t. a) Chels up 506.2 rocket la a) After how much time does the ball hit the a) Who wins the rocket race? (What is the Round to the nearest tenth. max height for both rockets?) b) what is the greatest height the ball b) After how many seconds does each rocket achieves? Round to the nearest tenth. land? a) approximately 6.7 seconds b) approximately 30.9 feet c) To the nearest tenth of a second, what was the difference in time for the two different rockets to reach their respective max heights? d D2W0[1d6g FKJuFtMaL ks^ocfktxwcadrxer QLbLkCM.F a nail^ln UrNi\gOhvtlsV ]rlews_errxv\eydt.g c NMtaldIew rwjixtwha ii^nxfaivnqidtfew ladlogfeibor_ap p2f. -3-