Question

5. James Rodriguez strikes a soccer ball during penalty kicks. The arc of the ball can be mapped by the function f(x) = −8t(t – 8). How long does the ball spend in the air?​

Answer 1

The function f(x) = -8t(t - 8) represents the height of the soccer ball at any given time t, where t is the time in seconds after the ball was kicked.

To find out how long the ball spends in the air, we need to determine the time at which the ball hits the ground. The ball hits the ground when its height is zero, so we can set f(x) = 0 and solve for t:

-8t(t - 8) = 0

This equation has two solutions: t = 0 and t = 8. The first solution corresponds to the time when the ball is kicked and the second solution corresponds to the time when the ball hits the ground. Since we're interested in the time the ball spends in the air, we need to subtract the time the ball was kicked from the time the ball hits the ground:

t = 8 - 0 = 8 seconds

Therefore, the ball spends 8 seconds in the air.