+360 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)=−4.9x^2+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)=−4.9x^2+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?
answer, rounded to the nearest tenth of a meter. m=
Thanks so much. Math is exhausting hard work that takes up my time. Im just trying to wrap my head around this
+36915 Since both of these equations describe height.....we are looking for the time when they are equal....so set them equal to each other and solve for x...this will be the time when they are at THE SAME HEIGHT...
-4.9x^2+12x+2.5 = -4.9x^2 +14x
12x+2.5 = 14x
2.5 = 2x
x = 2.5/2 = 1.25 seconds
Not done yet......this is the TIME when they are at the same height....we need to sub this value of x into one of the equations to find the height at this time
-4.9(1.25)^2 + 14 (1.25) = ~~ 9.8 m
+36915 Since both of these equations describe height.....we are looking for the time when they are equal....so set them equal to each other and solve for x...this will be the time when they are at THE SAME HEIGHT...
-4.9x^2+12x+2.5 = -4.9x^2 +14x
12x+2.5 = 14x
2.5 = 2x
x = 2.5/2 = 1.25 seconds
Not done yet......this is the TIME when they are at the same height....we need to sub this value of x into one of the equations to find the height at this time
-4.9(1.25)^2 + 14 (1.25) = ~~ 9.8 m
