Question

Arnold kicks a soccer ball from the top of an 8-foot platform onto the field below. The height, h, of the ball is given by the

function h(t) = -16t² + 16t+8, where t is the number of seconds after the ball is kicked.
How long does the ball stay in the air before it hits the ground?

Answer 1

To determine how long the soccer ball stays in the air after being kicked from an 8-foot platform, we solve the quadratic equation -16t² + 16t + 8 = 0. The ball stays in the air for 1 second before hitting the ground.

Step-by-step explanation:

The student's question about the time a soccer ball stays in the air after being kicked from an 8-foot platform can be solved using the given quadratic function h(t) = -16t² + 16t + 8. To find out for how long the ball remains in the air before hitting the ground, we need to determine when the height h becomes zero, which is when the ball touches the ground.

Setting the function equal to zero and solving for t, we get:

0 = -16t² + 16t + 8

This is a quadratic equation which can be solved using the quadratic formula: t = (-b ± √(b² - 4ac)) / (2a). The coefficients are a = -16, b = 16, and c = 8.

Applying the formula:

t = (-16 ± √(16² - 4*(-16)*8)) / (2*(-16))

Simplifying and choosing the positive root gives us the time the ball stays in the air:

t = 1 second