Assertion : A body droped from a given height and another body projected horizontal from the same height strike the ground simultaneously
Reason : Because horizontal velocity has no effect in the vertical direction .

Options

A. If both assertion `&` Reason are True `&` the Reason is a corrrect explanation of the Asserion.
B. If both Assertion `&` Reason are True but Reason is not correct explanation of the Assertion.
C. If Assertion is Trie but the Reason is False.
D. If both Assertion `&` Reason are false

Answer

To solve the assertion and reason question, we will analyze both statements step by step.

### Step 1: Understand the Assertion
The assertion states that a body dropped from a height and another body projected horizontally from the same height will strike the ground simultaneously.

### Step 2: Analyze the Motion of Both Bodies
1. **Body Dropped Vertically**:
- When the first body is dropped, it starts from rest (initial vertical velocity, \( u_y = 0 \)).
- The only force acting on it is gravity, which accelerates it downwards with an acceleration \( g \).
- The time taken to reach the ground can be calculated using the equation of motion:
\[ h = u_y t + \frac{1}{2} g t^2 \]
- Since \( u_y = 0 \), the equation simplifies to:
\[ h = \frac{1}{2} g t^2 \]

2. **Body Projected Horizontally**:
- The second body is projected horizontally from the same height. Its initial vertical velocity is also \( u_y = 0 \).
- Similar to the first body, the only force acting on it is gravity, causing it to fall with the same acceleration \( g \).
- The time taken to reach the ground is also given by the same equation:
\[ h = \frac{1}{2} g t^2 \]

### Step 3: Compare the Times
- Since both bodies are falling from the same height \( h \) and are subject to the same gravitational acceleration \( g \), the time \( t \) taken for both bodies to hit the ground is the same.

### Step 4: Understand the Reason
The reason states that horizontal velocity has no effect on the vertical motion. This is true because:
- The horizontal motion and vertical motion are independent of each other in projectile motion.
- The horizontal velocity only affects how far the body travels horizontally, not how quickly it falls vertically.

### Conclusion
Both the assertion and reason are correct:
- The assertion is true because both bodies take the same time to fall to the ground.
- The reason is also true as it correctly explains why the horizontal velocity does not affect the vertical fall.

### Final Answer
Both the assertion and reason are true, and the reason is the correct explanation of the assertion.

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