To determine the maximum height reached by the ball when thrown vertically upward, we can use the following kinematic equation:
Final velocity squared (v_f^2) = Initial velocity squared (v_i^2) + 2 * acceleration (a) * displacement (d)
In this case, the ball is thrown vertically upward, so its final velocity (v_f) will be zero at the highest point of its trajectory. The initial velocity (v_i) is given as 196 m/s. The acceleration (a) is the acceleration due to gravity, which is approximately -9.8 m/s² (negative because it acts in the opposite direction to the motion). We want to find the displacement (d), which represents the height the ball reaches.
Rearranging the equation, we have:
0 = (196 m/s)^2 + 2 * (-9.8 m/s²) * d
Simplifying:
0 = 38416 m²/s² - 19.6 m/s² * d
19.6 m/s² * d = 38416 m²/s²
d = 38416 m²/s² / 19.6 m/s²
d ≈ 1960.8 m
Therefore, the ball rises to a height of approximately 1960.8 meters.