Chapter 2.2, Problem 32AE

Granny Shots The last player in the NBA to use an underhand foul shot (a “granny� shot) was Hall of Fame forward Rick Barry, who retired in 1980. Barry believes that current NBA players could increase their free-throw percentage if they were to use an underhand shot. Since underhand shots are released from a lower position, the angle of the shot must be increased. If a player shoots an underhand foul shot, releasing the ball at a 70-degree angle from a position 3.5 feet above the floor, then the path of the ball can be modeled by the function

$h\left(x\right)=-\frac{136x^2}{v^2}+2.7x+3.5$, 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.

(a) The center of the hoop is 10 feet above the floor and 15 feet in front of the foul line. Determine the initial velocity with which the ball must be shot in order for the ball to go through the hoop.

(b) Write the function for the path of the ball using the velocity found in part (a).

(c) Determine the height of the ball after it has traveled 9 feet in front of the foul line.

(d) Find additional points and graph the path of the basketball.

Source: The Physics of Foul Shots, Discover, Vol. 21, No. 10, October 2000