(A):A body thrown up from the top of a tower and another body thrown down from the same point strike the ground witht the same velocity.
(R ):Initial speed and acceleration are common for both.

Answer

To solve the problem, we will analyze the two bodies thrown from the top of a tower: one thrown upwards and the other thrown downwards. We will show that they strike the ground with the same velocity.

### Step-by-Step Solution:

1. **Identify the Variables**:
- Let the height of the tower be \( h \).
- Let the initial speed of both bodies be \( U \).
- The acceleration due to gravity is \( g \).

2. **Analyze the Body Thrown Upwards**:
- When the body is thrown upwards, its initial velocity is \( -U \) (negative because it is opposite to the direction of gravity).
- The acceleration due to gravity is \( -g \) (also negative).
- The equation of motion for this body is:
\[ V_1^2 = U^2 + 2a s \]
Here, \( a = -g \) and \( s = -h \) (the displacement is negative as it moves upwards before falling down). Thus:
\[ V_1^2 = (-U)^2 + 2(-g)(-h) \]
Simplifying this gives:
\[ V_1^2 = U^2 + 2gh \]
Therefore, the final velocity \( V_1 \) when it strikes the ground is:
\[ V_1 = \sqrt{U^2 + 2gh} \]

3. **Analyze the Body Thrown Downwards**:
- For the body thrown downwards, its initial velocity is \( U \) (positive).
- The acceleration due to gravity is \( g \) (positive).
- The equation of motion for this body is:
\[ V_2^2 = U^2 + 2gh \]
Therefore, the final velocity \( V_2 \) when it strikes the ground is:
\[ V_2 = \sqrt{U^2 + 2gh} \]

4. **Compare the Velocities**:
- From the calculations, we see that:
\[ V_1 = \sqrt{U^2 + 2gh} \]
\[ V_2 = \sqrt{U^2 + 2gh} \]
- Thus, \( V_1 = V_2 \). This means both bodies strike the ground with the same velocity.

5. **Conclusion**:
- The assertion that a body thrown up from the top of a tower and another body thrown down from the same point strike the ground with the same velocity is true.
- The reason that initial speed and acceleration are common for both is also true, and it correctly explains the assertion.