document.write( "Question 1183238: Hayden is playing with a toy airplane. The height of the airplane, in metres, is given by the relation
\n" ); document.write( "h = −5t^2+ 18t + 1, where t is the number of seconds since the plane was launched. At time t, the
\n" ); document.write( "horizontal distance travelled by the airplane is given by d = 4. 5t.
\n" ); document.write( "a) For how long will the airplane be in the air, rounded to the nearest tenth of a second?
\n" ); document.write( "b) How far will the airplane travel horizontally by the time it hits the ground, rounded to the
\n" ); document.write( "nearest tenth of a
\n" ); document.write( " metre?
\n" ); document.write( "c) At what time(s), rounded to the nearest tenth of a second, will the airplane reach a height of
\n" ); document.write( " 12 m?
\n" ); document.write( "d) What is the maximum height or the plane? \n" ); document.write( "

Algebra.Com's Answer #813458 by ikleyn(52786) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "Hayden is playing with a toy airplane. The height of the airplane, in metres, is given by the relation
\n" ); document.write( "h = −5t^2+ 18t + 1, where t is the number of seconds since the plane was launched. At time t, the
\n" ); document.write( "horizontal distance travelled by the airplane is given by d = 4.5t.
\n" ); document.write( "a) For how long will the airplane be in the air, rounded to the nearest tenth of a second?
\n" ); document.write( "b) How far will the airplane travel horizontally by the time it hits the ground, rounded to the nearest tenth of a metre?
\n" ); document.write( "c) At what time(s), rounded to the nearest tenth of a second, will the airplane reach a height of 12 m?
\n" ); document.write( "d) What is the maximum height or the plane?
\n" ); document.write( "~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "From the equations, the initial vertical speed is 18 m/s up; the initial height is 1 meter (at the start);\r
\n" ); document.write( "\n" ); document.write( "horizontal speed is 4.5 m/s, the constant value during the flight.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "a) For how long will the airplane be in the air, rounded to the nearest tenth of a second? \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "    The toy airplane is in the air until h(t) > 0.  The airplane get the ground when h(t) = 0.\r\n" );
document.write( "\r\n" );
document.write( "    THEREFORE, to find the time the airplane is in the air, we should solve this quadratic equation\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "        -5t^2 + 18t + 1 = 0\r\n" );
document.write( "\r\n" );
document.write( "         =  = .\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    Of the two roots, we chose the positive one, which is  t =  = 3.7 seconds  (rounded as requested).   \r\n" );
document.write( "\r\n" );
document.write( "    So, question (a) is answered: the airplane is in the air 3.7 seconds.\r\n" );
document.write( "

\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "b) How far will the airplane travel horizontally by the time it hits the ground, rounded to the nearest tenth of a metre? \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "    Simply multiply the horizontal component of the speed by the time\r\n" );
document.write( "\r\n" );
document.write( "        horizontal distance = 4.5 * 3.7 = 16.45 meters.    ANSWER\r\n" );
document.write( "

\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "c) At what time(s), rounded to the nearest tenth of a second, will the airplane reach a height of 12 m? \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "    To answer, we should solve this quadratic equation    \r\n" );
document.write( "\r\n" );
document.write( "        -5t^2 + 18t + 1 = 12\r\n" );
document.write( "\r\n" );
document.write( "        -5t^2 + 18t - 11 = 0\r\n" );
document.write( "\r\n" );
document.write( "          =  = .\r\n" );
document.write( "\r\n" );
document.write( "          =  = 0.78 s;   =  = 2.82 s.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "         The smaller value of t is the ascending flight;  the larger value of t is the descending flight.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "         Part (c) is completed.\r\n" );
document.write( "

\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "d) What is the maximum height or the plane?\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "    The highest point of the flight is the vertex of the quadratic function h(t).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    The value of \"t\"  is  t = \"  \" =  =  = 1.8.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    It means that the airplane reaches the maximum height at t= 1.8 seconds.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    The maximum height is the value of the height function at t= 1.8\r\n" );
document.write( "\r\n" );
document.write( "         =  = 17.2 meters.     ANSWER\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "The problem is just solved.     //     All questions are answered.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "==================\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "To see many other solved similar and different problems, see the lessons\r
\n" ); document.write( "\n" ); document.write( "    - Introductory lesson on a projectile thrown-shot-launched vertically up \r
\n" ); document.write( "\n" ); document.write( "    - Problem on a projectile moving vertically up and down\r
\n" ); document.write( "\n" ); document.write( "    - Problem on an arrow shot vertically upward\r
\n" ); document.write( "\n" ); document.write( "    - Problem on a ball thrown vertically up from the top of a tower \r
\n" ); document.write( "\n" ); document.write( "    - Problem on a toy rocket launched vertically up from a tall platform\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "    - Problem on a projectile thrown horizontally \r
\n" ); document.write( "\n" ); document.write( "    - Problems on projectile launched at an angle to horizon \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Consider these lessons as your textbook, handbook, tutorials and (free of charge) home teacher.
\n" ); document.write( "Read them attentively and learn how to solve this type of problems once and for all.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Also, you have this free of charge online textbook in ALGEBRA-I in this site\r
\n" ); document.write( "\n" ); document.write( "    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "The referred lessons are the part of this textbook under the topic \"Projectiles launched/thrown and moving vertically up and dawn\".\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Save the link to this online textbook together with its description\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Free of charge online textbook in ALGEBRA-I
\n" ); document.write( "https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "to your archive and use it when it is needed.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );