To find the maximum height reached by the ball, we can use the equations of motion for projectile motion.
In this case, the ball is thrown vertically upwards, so we only need to consider the vertical motion. The equation to calculate the maximum height is:
h = (v^2 - u^2) / (2 * g)
Where: h is the maximum height v is the final velocity (0 m/s at the highest point) u is the initial velocity (64 feet/s) g is the acceleration due to gravity (32.2 feet/s^2)
Let's substitute the given values into the equation and calculate the maximum height:
h = (0^2 - 64^2) / (2 * 32.2) h = (-4096) / (64.4) h ≈ -63.54 feet
The negative sign indicates that the height is measured below the initial position. However, since we're interested in the maximum height reached by the ball, we take the absolute value:
Maximum height ≈ |-63.54| feet Maximum height ≈ 63.54 feet
Therefore, the maximum height reached by the ball is approximately 63.54 feet.