A ball is thrown vertically upward with a velocity of 20 m/s. Calculate the maximum height attain by the ball.

Explanation

To solve the problem of calculating the maximum height attained by a ball thrown vertically upward with an initial velocity of 20 m/s, we can use the following steps:

### Step 1: Understand the given values
- Initial velocity (U) = 20 m/s (upward)
- Final velocity (V) at maximum height = 0 m/s (the ball stops rising at the maximum height)
- Acceleration (A) = -g = -9.8 m/s² (the acceleration due to gravity acts downward)

### Step 2: Use the kinematic equation
We can use the kinematic equation that relates initial velocity, final velocity, acceleration, and displacement (height in this case):
\[ V^2 = U^2 + 2AH \]
Where:
- \( H \) is the maximum height attained.

### Step 3: Substitute the known values into the equation
Substituting the known values into the equation:
\[ 0^2 = (20)^2 + 2(-9.8)H \]

### Step 4: Simplify the equation
This simplifies to:
\[ 0 = 400 - 19.6H \]

### Step 5: Solve for H
Rearranging the equation gives:
\[ 19.6H = 400 \]
\[ H = \frac{400}{19.6} \]

### Step 6: Calculate H
Calculating the value:
\[ H \approx 20.41 \text{ meters} \]

### Final Answer
The maximum height attained by the ball is approximately **20.41 meters**.

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