To determine the maximum height the ball can reach when thrown vertically upward with an initial velocity of 15 m/s, we can use the equations of motion for vertical motion under constant acceleration.
The key equation we'll use is:
v^2 = u^2 + 2as
where: v is the final velocity, u is the initial velocity, a is the acceleration, and s is the displacement.
In this case, the ball is thrown upward, so the acceleration due to gravity (-9.8 m/s^2) acts in the opposite direction to the motion.
At the maximum height, the final velocity (v) of the ball will be zero. Therefore, we have:
0 = (15 m/s)^2 + 2(-9.8 m/s^2)s
Simplifying the equation:
0 = 225 - 19.6s
19.6s = 225
s = 225 / 19.6
s ≈ 11.48 meters
Thus, the ball can reach a maximum height of approximately 11.48 meters when thrown vertically upward with an initial velocity of 15 m/s.