A ball is launched from the ground vertically into the air with a speed of 10 m/s. Calculate the maximum height of the ball.

1. Use the kinematic equation:

v^2 = u^2 + 2as

2. Substitute the values (\( v = 0 \), \( u = 10 \), \( a = -9.8 \)):

0 = 10^2 + 2(-9.8)s

3. Simplify the equation:

0 = 100 - 19.6s

4. Solve for \( s \):

19.6s = 100

s = \frac{100}{19.6}

s \approx 5.10

Answer: The maximum height of the ball is s \approx 5.10 meters.