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42) A Little League baseball player throws a ball upward. The height h of the ball (in feet) t seconds after the ball is released is given by h 16t2 30t 4. a) What is the initial height of the ball? 4 ft b) When is the ball 18 feet above the ground? when t 7 8 sec and when t 1 sec c) How long does it take for the ball to hit the ground? 2 sec Organizers of fi reworks shows use quadratic and linear equations to help them design their programs. Shells contain the chemicals that produce the bursts we see in the sky. At a fi reworks show, the shells are shot from mortars and when the chemicals inside the shells ignite, they explode, producing the brilliant bursts we see in the night sky. 75° 43) At a fi reworks show, a 3-in. shell is shot from a mortar at an angle of 75. The height, y (in feet), of the shell t sec after being shot from the mortar is given by the quadratic equation y 16t2 144t and the horizontal distance of the shell from the mortar, x (in feet), is given by the linear equation x 39t (http://library.thinkquest.org/15384/physics/physics.html) a) How high is the shell after 3 sec? 288 ft b) What is the shell’s horizontal distance from the mortar after 3 sec? 117 ft c) The maximum height is reached when the shell explodes. How high is the shell when it bursts after 4.5 sec? 324 ft d) What is the shell’s horizontal distance from its launching point when it explodes? (Round to the nearest foot.) 176 ft 44) When a 10-in. shell is shot from a mortar at an angle of 75, the height, y (in feet), of the shell t sec after being shot from the mortar is given by y 16t2 264t and the horizontal distance of the shell from the mortar, x (in feet), is given by x 71t a) How high is the shell after 3 sec? 648 ft b) Find the shell’s horizontal distance from the mortar after 3 sec. 213 ft c) The shell explodes after 8.25 sec. What is its height when it bursts? 1089 ft d) What is the shell’s horizontal distance from its launching point when it explodes? (Round to the nearest foot.) 586 ft e) Compare your answers to 43a) and 44a). What is the difference in their heights after 3 sec? 360 ft f) Compare your answers to 43c) and 44c). What is the difference in the shells’ heights when they burst? 765 ft g) Use the information from Exercises 43 and 44. Assuming that the technicians timed the fi rings of the 3-in. shell and the 10-in. shell so that they exploded at the same time, how far apart would their respective mortars need to be so that the 10-in. shell would burst directly above the 3-in. shell? 45) An object is launched upward with an initial velocity of 96 ft/sec. The height h (in feet) of the object after t seconds is given by h 16t2 96t. a) From what height is the object launched? 0 ft b) When does the object reach a height of 128 ft? after 2 sec and after 4 sec c) How high is the object after 3 sec? 144 ft d) When does the object hit the ground? after 6 sec 46) An object is launched upward with an initial velocity of 128 ft/sec. The height h (in feet) of the object after t seconds is given by h 16t2 128t. a) From what height is the object launched? 0 ft b) Find the height of the object after 2 sec. 192 ft c) When does the object hit the ground? after 8 sec www.mhhe.com/messersmith SECTION 7.6 Applications of Quadratic Equations 441


messersmith_power_introductory_algebra_1e_ch4_7_10
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