There is a tower of height 20m and a particle is projected up from top of the tower with an initial speed 20m//s. Top of the tower is marked as point A, from where particle is projected. Point of maximum height a denoted as B. When particle reaches the point A during downward journey then we call the same point as C. Point at the bottom of tower is marked as Dwhere particle finally strikes. Acceleration due to gravity `g=10m//s^(2)`
Maximum height above the ground attained by particle is

Options

A. 20m
B. 30m
C. 40m
D. 60m

Explanation

To solve the problem step by step, we will analyze the motion of the particle projected from the top of the tower and calculate the maximum height it reaches above the ground.

### Step 1: Understand the Given Information
- Height of the tower (h_tower) = 20 m
- Initial speed of the particle (u) = 20 m/s (upward)
- Acceleration due to gravity (g) = 10 m/s² (downward)

### Step 2: Identify Points
- Point A: Top of the tower (where the particle is projected)
- Point B: Maximum height reached by the particle
- Point C: Point A during the downward journey (when the particle returns to the top of the tower)
- Point D: Ground level (bottom of the tower)

### Step 3: Calculate the Maximum Height (h_max) Above Point A
We will use the third equation of motion to find the maximum height reached by the particle above point A (h_max):
\[ v^2 = u^2 + 2as \]
Where:
- v = final velocity at maximum height = 0 m/s (at point B)
- u = initial velocity = 20 m/s
- a = acceleration = -g = -10 m/s² (negative because it is acting downward)
- s = displacement from A to B = h_max

Substituting the values into the equation:
\[ 0 = (20)^2 + 2(-10)(h_{max}) \]
\[ 0 = 400 - 20h_{max} \]
\[ 20h_{max} = 400 \]
\[ h_{max} = \frac{400}{20} = 20 \text{ m} \]

### Step 4: Calculate the Total Maximum Height Above Ground
The total maximum height (H_total) above the ground is the sum of the height of the tower and the maximum height reached above point A:
\[ H_{total} = h_{tower} + h_{max} \]
\[ H_{total} = 20 \text{ m} + 20 \text{ m} = 40 \text{ m} \]

### Final Answer
The maximum height attained by the particle above the ground is **40 meters**.

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