To determine the maximum height reached by the ball when thrown straight up, we can use the equations of motion. The key equation in this case is:
v^2 = u^2 + 2as
where: v = final velocity (which is 0 m/s when the ball reaches its highest point) u = initial velocity a = acceleration (in this case, acceleration due to gravity, which is approximately -9.8 m/s^2) s = displacement (maximum height reached by the ball)
Rearranging the equation, we have:
0 = (36.12)^2 + 2(-9.8)s
Simplifying the equation:
0 = 1305.8544 - 19.6s
19.6s = 1305.8544
s = 1305.8544 / 19.6
s ≈ 66.69 meters
Therefore, the ball will reach a maximum height of approximately 66.69 meters.