HW Quadratics review- what we know so far 1. A rocket is launched with an initia
ID: 2919604 • Letter: H
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HW Quadratics review- what we know so far 1. A rocket is launched with an initial velocity of 110 m/s. The height of the rocket in meters is approximated by the quadratic equation hSt +110t where t is the time after launch in seconds About how long does it take for the rocket to return to the ground? 2. A hammer is dropped from a 49 ft scaffold. The function h(t) 16 49 represents the height of the hammer. Find out when the hammer reaches the ground. 3. Robert threw the rock to enter the water. a rock off a bridge into the river. The distance from the rock to the river is modeled by the equation h - -16- 16t+ 60, where h is the height in feet and t is the time in seconds. Find how long it took 4. A group of friends are launching water balloons from the roof of the school bullding. The function ft)-6t-96 + 20 represents the height (in feet) of the balloon t seconds after it is launched. How long was the balloon in the air?Explanation / Answer
The rocket returns to the ground when h = 0, i.w. when -5t2+100t = 0 or, t(110-5t) = 0. Thus, t = 0 ( when the rocket is fired) or, 5t = 110 so that t = 110/5 = 22.Thus, the rocket will return to the ground after 22 seconds. The hammer reaches the ground when h(t) = 0, i.e. when -16t2+49 = 0 or, 16t2 = 49 or, t2 =49/16 so that t = 7/4 = 1.75. Thus, the hammer will reache the ground after 7/4 or, 1.75 seconds. The rock will hit the water when h(t)=0, i.e.when -16t2-16t+60=0 or,4t2+4t-15 = 0 or, 4t2+10t-6t-15 = 0 or, 2t(2t+5)-3(2t+5) = 0 or, (2t-3)(2t+5) = 0. Since t cannot be negative, hence 2t = 3 or, t = 3/2 = 1.5. Thus, the rock will hit the water after 1.5 seconds. There is a misprint. We must have f(t) = -16t2+9t+20 or, -16t2+96t+20. In the absence of the suffix t,the two numbers 96 and 20 do not make any sense. These may as well be combined to become 116. We presume that f(t) = -16t2+9t+20. The ballon will hit the hit the ground when f(t) = 0, i.e. -16t2+9t+20 = 0 or, 16t2-9t -20 = 0. On using the quadratic formula, we get t = [9±?(81+4*16*20)]/32 = [9±?1361]/32 = (9±36.89)/32 = (9+36.89)/32 ( as t cannot be negative) = 45.89/32= 1.43 seconds.
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