A stone is thrown vertically up from the top of the tower with velocity 20m/s reaches the ground in 6 seconds,find the height of the tower

To determine the height of the tower from which the stone is thrown, we can apply kinematic equations with gravity acting as an acceleration in the downward direction.

Given dataTo determine the height of the tower from which the stone is thrown, we can apply kinematic equations with gravity acting as an acceleration in the downward direction.

Given 
- Initial velocity of the stone, \( u = 20 \, \text{m/s} \) (upward)
- Time taken to reach the ground, \( t = 6 \, \text{s} \)
- Acceleration due to gravity, \( g = 9.8 \, \text{m/s}^2 \)

Since the stone is thrown upwards, its initial velocity will reduce to zero at its peak, then it will accelerate downwards due to gravity.

### Step-by-Step Solution

1. **Total Displacement Calculation Using Kinematics**:
   Using the equation for displacement with constant acceleration:
   \[
   s = ut + \frac{1}{2} a t^2
   \]
   where:
   - \( s \) is the displacement,
   - \( u \) is the initial velocity,
   - \( a \) is the acceleration (here, \( -9.8 \, \text{m/s}^2 \) since it’s downwards),
   - \( t \) is the total time.

   Substitute the values:
   \[
   s = (20 \times 6) + \frac{1}{2} \times (-9.8) \times (6^2)
   \]
   
2. **Calculation**:
   - First term: \( 20 \times 6 = 120 \, \text{m} \)
   - Second term: \( \frac{1}{2} \times -9.8 \times 36 = -176.4 \, \text{m} \)

   So, \( s = 120 - 176.4 = -56.4 \, \text{m} \).

The negative sign indicates that the stone ends up 56.4 meters below its starting point, meaning the height of the tower is **56.4 meters**.

Would you like further details or have any questions?

Here are some related questions you might find interesting:
1. How would the height of the tower change if the initial velocity were different?
2. What would happen if the stone were thrown downwards instead of upwards?
3. How would air resistance affect the time taken to reach the ground?
4. Can we calculate the maximum height the stone reaches before falling back down?
5. How would this calculation change if gravity were not constant?

**Tip:** When solving kinematic problems, carefully choose the sign for acceleration to match its direction relative to your initial setup.

A stone is thrown vertically up from the top of the tower with velocity 20m/s reaches the ground in 6 seconds, find the height of the tower.

Learn how to find the height of a tower by analyzing the motion of a stone thrown upwards with an initial velocity of 20 m/s and a fall time of 6 seconds. This kinematics problem involves understanding projectile motion, gravity's impact, and displacement calculation. Ideal for students in Grades 9-12.

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