To determine how high the ball rises when thrown vertically upward with a velocity of 98 m/s, we can use the kinematic equation that relates displacement, initial velocity, final velocity, and acceleration:
v^2 = u^2 + 2as
Where: v is the final velocity (0 m/s when the ball reaches its highest point) u is the initial velocity (98 m/s) a is the acceleration due to gravity (-9.8 m/s^2, taking negative since it opposes the motion) s is the displacement or height we want to find.
Rearranging the equation, we have:
0^2 = (98 m/s)^2 + 2(-9.8 m/s^2)s
Simplifying:
0 = 9604 m^2/s^2 - 19.6 m/s^2 * s
19.6 m/s^2 * s = 9604 m^2/s^2
s = 9604 m^2/s^2 / 19.6 m/s^2
s ≈ 490.8 m
Therefore, the ball rises to a height of approximately 490.8 meters.