Final answer:
The equation h(s) = -3s² + 75 represents the height of a soccer ball after s seconds. To find the time it takes for the ball to hit the ground, we set h(s) equal to 0 and solve for s. It will take the soccer ball approximately 3.79 seconds to hit the ground.
Step-by-step explanation:
The equation h(s) = -3s² + 75 represents the height of a soccer ball after s seconds. To find the time it takes for the ball to hit the ground, we set h(s) equal to 0 and solve for s.
-3s² + 75 = 0
solving this quadratic equation, we can use the quadratic formula: s = (-b ± √(b² - 4ac)) / (2a).
Using the values from the equation, a = -3, b = 0, and c = 75, we can calculate the values of s.
s₁ = (-0 + √(0² - 4*(-3)*75)) / (2*(-3)) = 3.79 seconds
s₂ = (-0 - √(0² - 4*(-3)*75)) / (2*(-3)) = 0.54 seconds
Since the ball is at a height of 10m at two different times during its trajectory, we take the longer solution for the time it takes the ball to hit the ground. Therefore, it will take the soccer ball approximately 3.79 seconds to hit the ground.