A football is kicked from the ground and travels at a rate of 10 meters per second. The function 𝑓(𝑥)=10𝑥−5𝑥2 represents the ball's height above the ground at x seconds. Based on this function model, what is the football's highest point and how long will it take to hit the ground?
4 answers
I think that the ball will reach 400 meters at the highest point and the ball will hit the ground in 40 seconds. Is this correct?
the max is on the axis of symmetry of the parabola
x = -b / 2 a = -10 / (2 * -5) = 1
1 second up, one second down ... 2 sec flight time
plug one into the original equation to find max height
x = -b / 2 a = -10 / (2 * -5) = 1
1 second up, one second down ... 2 sec flight time
plug one into the original equation to find max height
F(x) = 10x-5x^2.
a. V^2 = Vo^2+2g*h = 0.
10^2+(-20)h = 0
h = 5 m. = max. ht.
b. 10x-5x^2 = 0 when the ball hits gnd.
Divide both sides by 5x:
2-x = 0
X = 2 s. to hit gnd.
a. V^2 = Vo^2+2g*h = 0.
10^2+(-20)h = 0
h = 5 m. = max. ht.
b. 10x-5x^2 = 0 when the ball hits gnd.
Divide both sides by 5x:
2-x = 0
X = 2 s. to hit gnd.
a. Yes, the original Eq should be used to calculate max. ht. :
h max = 10x-5x^2 = 10*1-5*1^2 =
h max = 10x-5x^2 = 10*1-5*1^2 =
1 answer