In American football, the ball is punted by dropping and kicking it before it hits the ground. The height h(t) of the football a
bove the ground in meters t seconds after being punted is affected by gravity and by the punter's kick, and can be represented as the difference of two functions: a(t)=1.4t2, which specifies the effect of gravity on the height of the ball, and v(t)=12.1t+2.5, which specifies the effect of the punt on the ball. With these two functions, h(t)=v(t)-a(t), how high above the ground was the ball when it was punted?
The height h(t) of the football above the ground in meters t seconds after being punted is affected by gravity and by the punters kick, and can be represented as the difference of two functions:
We need to find h(t) such that, h(t)=v(t)-a(t)
So,
It is a quadratic equation. When we solve it we get :
Neglecting negative value,
h(t) = 8.845 m
So, the ball was at a height of 8.845 m when it was punted.