To determine how long the ball will take to reach its maximum height, we need to consider the motion of the ball under gravity.
When the ball is thrown vertically upward, its initial velocity is 15 m/s. Due to the force of gravity acting on it, the ball's velocity decreases until it reaches its maximum height and then starts falling back down.
At the maximum height, the ball momentarily comes to a stop before starting its downward descent. This means that the ball's final velocity at the maximum height is 0 m/s.
We can use the kinematic equation for vertical motion to calculate the time taken to reach the maximum height:
vf = vi + at
where: vf = final velocity (0 m/s at the maximum height) vi = initial velocity (15 m/s) a = acceleration (due to gravity, -9.8 m/s^2, negative because it acts opposite to the motion) t = time
Substituting the known values into the equation:
0 = 15 - 9.8t
Rearranging the equation to solve for time:
9.8t = 15
t = 15 / 9.8
t ≈ 1.53 seconds
Therefore, it will take approximately 1.53 seconds for the ball to reach its maximum height.