Eli and Karl each throw a basketball straight up in the air at the same time. Eli is standing on a deck and the height of his ball, in meters, is given by the function f(x)=−4.9x2+12x+2.5 , where x is the number of seconds after the ball is released from his hands. Karl is standing on the ground and the height of his ball, in meters, is given by the function g(x)=−4.9x2+14x , where x is the number of seconds after the ball is released from his hands.There is a moment when the basketballs are at the same height.What is this height?Enter your answer, rounded to the nearest tenth of a meter, in the box.

We are to find the time at which the height of basketball thrown by Eli and Karl is equal. We have the functions which model the heights of both basketballs. So by equating the functions representing the height of both basketballs we can find the value of x from that equation at which the height is same for both basketballs.

[tex]-4.9 x^{2} +12x+2.5=-4.9 x^{2} +14x \\ \\ 12x+2.5=14x \\ \\ 2.5=2x \\ \\ x=1.25[/tex]

Thus after 1.25 seconds the height of basketballs thrown by Eli and Karl will be at the same height. This can be verified by finding the heights of both at x=1.25

For Eli:
[tex]Height=f(1.25)=-4.9 (1.25)^{2}+12(1.25)+2.5=9.84375 [/tex]

For Karl:
[tex]Height=f(1.25)=-4.9 (1.25)^{2}+14(1.25)=9.84375 [/tex]

Thus height of both basketball is equal after 1.25 seconds