To find out how long it will take for the ball to reach the friend who is 20 feet below, we can use the given equation: h = -16t² + vt + s.
In this case, the initial velocity v is 10 feet per second (given as 10 ft/s), and the initial height s is 0 (since the ball is thrown out of a window).
Now, we need to find the time t when the height h is equal to 20 feet (the height of the friend).
Substitute h = 20, v = 10, and s = 0 into the equation:
20 = -16t² + 10t
Next, rearrange the equation to set it equal to zero by moving 20 to the other side:
-16t² + 10t - 20 = 0
To solve this quadratic equation, you can use the quadratic formula:
t = [-b ± √(b² - 4ac)] / 2a
In this case, a = -16, b = 10, and c = -20.
Plug in these values to find the roots of the equation.
Calculate the discriminant (b² - 4ac) first to determine the nature of the roots:
Discriminant = 10² - 4*(-16)*(-20)
Discriminant = 100 - 1280
Discriminant = -1180
Since the discriminant is negative, the roots will be complex, meaning the ball will never reach the friend 20 feet below.
Therefore, the ball thrown by the lacrosse player will not reach the friend on the ground.
