To determine how long it will take for the ball to reach its maximum height, we need to use the equation of motion for vertical motion under constant acceleration. In this case, the acceleration due to gravity is acting in the opposite direction to the ball's initial velocity. The equation is:
v = u + at
Where:
- v is the final velocity (0 m/s at the maximum height because the ball momentarily comes to a stop).
- u is the initial velocity (25 m/s, upward in this case).
- a is the acceleration due to gravity (-9.8 m/s² on Earth, acting downward).
- t is the time taken.
Substituting the values into the equation:
0 = 25 - 9.8t
Rearranging the equation to solve for t:
9.8t = 25
t = 25 / 9.8
Using a calculator, we find that t ≈ 2.55 seconds.
Therefore, it will take approximately 2.55 seconds for the ball to reach its maximum height.