Arianna kicks a soccer ball off the ground and in the air with an initial velocity of 42 feet per second. Approximately what maximum height does the soccer ball reach?
To determine the maximum height the soccer ball reaches, we can use kinematic equations. In this case, since we know the initial velocity and we want to find the maximum height (where the velocity becomes zero), we can use the equation:
v^2 = u^2 + 2as
Where:
v = final velocity (which is 0, since the ball reaches maximum height)
u = initial velocity (42 feet per second)
a = acceleration (in this case, the acceleration due to gravity, which is -32 feet per second squared, considering downward direction as negative)
s = displacement (maximum height)
Rearranging the equation, we have:
0^2 = (42)^2 + 2(-32)s
Expanding the equation:
0 = 1764 - 64s
Rearranging again:
64s = 1764
Dividing both sides by 64:
s = 27.56
Approximately, the maximum height the soccer ball reaches is 27.56 feet.