Nancy throws a ball toward a basket 3.2 m off the ground. The rule associated with the ball's trajectory is #y = -.4(x-6)^2 + 3.6#. Nancy throws the ball at a distance of 3 m from the basket. From what height did Nancy throw the ball?

1 Answer
Mar 12, 2018

Assuming we don't have to travel into the basket on the downward arc, Nancy threw the ball from a height of 2m

Explanation:

First, we need to know what the x value is in the trajectory equation that satisfies the basket height (#y=3.2#):

#3.2=3.6-0.4(x-6)^2#
#-0.4=-0.4(x-6)^2#
#x-6=1 rArr x=7#

we know that Nancy threw the ball 3m from the basket, meaning she was at a distance of #7-3=4m#. Plugging that into the trajectory equation gives us our launch height:

#y=3.6-0.4(4-6)^2 rArr y=3.6-0.4(-2)^2#
#y=3.6-0.4*4 rArr y=3.6-1.6#
#color(red)(y=2m)#