If a basketball player shoots a foul shot, releasing the ball at a $$ 45 $$ -degree angle from a position $$ 6 $$ feet above the floor, then the path of the ball can be modeled by the quadratic function, $$ h ( x ) = - \frac { 44 x ^ { 2 } } { v ^ { 2 } } + x + 6 $$ , where $$ h $$ is the height of the ball above the floor, $$ x $$ is the forward distance of the ball in front of the foul line, and $$ v $$ is the initial velocity with which the ball is shot in feet per second. Suppose a player shoots a ball with an initial velocity of $$ 27 $$ feet per second. (a) Determine the height of the ball after it has traveled $$ 7 $$ feet in front of the foul line. The height of the ball is ________ft. (Round to two decimal places as needed.) (b) Determine the height of the ball after it has traveled $$ 9 $$ feet in front of the foul line. The height of the ball is ________ft . (Round to two decimal places as needed.)

Question

If a basketball player shoots a foul shot, releasing the ball at a $$ 45 $$ -degree angle from a position $$ 6 $$ feet above the floor, then the path of the ball can be modeled by the quadratic function, $$ h ( x ) = - \frac { 44 x ^ { 2 } } { v ^ { 2 } } + x + 6 $$ , where $$ h $$ is the height of the ball above the floor, $$ x $$ is the forward distance of the ball in front of the foul line, and $$ v $$ is the initial velocity with which the ball is shot in feet per second. Suppose a player shoots a ball with an initial velocity of $$ 27 $$ feet per second. (a) Determine the height of the ball after it has traveled $$ 7 $$ feet in front of the foul line. The height of the ball is ________ft. (Round to two decimal places as needed.) (b) Determine the height of the ball after it has traveled $$ 9 $$ feet in front of the foul line. The height of the ball is ________ft . (Round to two decimal places as needed.)

Gardner Macdonald · Accepted Answer

(a) $$10.04 ft$$ (b) 10.11 ft

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