document.write( "Question 1087259:
\n" ); document.write( "A toy rocket is launched from the top of a building 67 feet tall at an initial velocity of 237 feet per second.
\n" ); document.write( "a) Give the function that describes the height of the rocket in terms of time t.
\n" ); document.write( "b) Determine the time at which the rocket reaches its maximum height, and the maximum height in feet.
\n" ); document.write( "c) For what time interval will the rocket be more than 6969 feet above ground level?
\n" ); document.write( "d) After how many seconds will it hit the ground? \n" ); document.write( "

Algebra.Com's Answer #701693 by jorel1380(3719) $\"\"$ $\"About$

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The equation for this rockets height at any time t (in seconds) would be:
\n" ); document.write( "a) h(t)=-4.9t²+237t+67
\n" ); document.write( "b) the maximum height of a projectile would be reached at a time of h(t)= at²+bt+c is given by the value -b/2a, which, in this case, would be -237/-9.8=24.184 seconds after launch.
\n" ); document.write( "The maximum height, given by the above equation, would be 2932.765 ft.
\n" ); document.write( "c)To find the time interval for when the rocket is above 69 ft., we use
\n" ); document.write( "69=-4.9t²+237t+67
\n" ); document.write( "4.9t²-237t+2=0
\n" ); document.write( "Using the quadratic formula, we get two roots of 48.3589066473 and 0.0084402914293 seconds. This gives us about 48 seconds where the rocket is higher than 69 ft.
\n" ); document.write( "d)h(t)=0=-4.9t²+237t+67
\n" ); document.write( "4.9t²-237t-67=0
\n" ); document.write( "Using the quadratic formula again, we get a positive value for t of 48.6484140538 seconds total flight time. ☺☺☺☺ \n" ); document.write( "

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