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STATEMENT-1: When a body is dropped and ...

STATEMENT-1: When a body is dropped and another body is thrown horizontally from the same height, it reaches the ground at the same time.
STATEMENT-2: They have same acceleration and same initial speed in vertical direction.

A

Statement-I is true, Statement-II is true, Statement-II is correct explanation for Statement-I

B

Statement-I is true, Statement-II is true, Statement-II is NOT a correct explanation for Statement-I

C

Statement-I is true, Statement-II is false

D

Statement-I is false, Statement-II is true.

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem, we need to analyze the two statements provided and determine their validity and relationship. ### Step-by-Step Solution: 1. **Understanding Statement 1**: - Statement 1 claims that when a body is dropped (let's call it Body A) and another body is thrown horizontally (let's call it Body B) from the same height, both bodies reach the ground at the same time. - This is true because the time taken for an object to fall solely depends on the height from which it is dropped and the acceleration due to gravity (g), not on the horizontal motion. **Hint**: Consider the factors that affect the time of flight for a falling object. 2. **Understanding Statement 2**: - Statement 2 states that both bodies have the same acceleration and the same initial speed in the vertical direction. - When Body A is dropped, its initial vertical speed (u) is 0 m/s. When Body B is thrown horizontally, its initial vertical speed is also 0 m/s. Both bodies experience the same gravitational acceleration (g) downwards. **Hint**: Analyze the initial velocities and accelerations of both bodies in the vertical direction. 3. **Time of Flight Calculation**: - The time of flight (t) for both bodies can be derived from the equation of motion under constant acceleration: \[ h = \frac{1}{2} g t^2 \] - Rearranging gives: \[ t = \sqrt{\frac{2h}{g}} \] - This shows that the time of flight depends only on the height (h) and the acceleration due to gravity (g), which are the same for both bodies. **Hint**: Recall the equations of motion for objects under constant acceleration. 4. **Conclusion**: - Since both bodies are subjected to the same gravitational acceleration and have the same initial vertical speed, they will indeed reach the ground at the same time. - Therefore, both statements are true, and Statement 2 correctly explains Statement 1. ### Final Answer: - **Option A**: Statement 1 is true, Statement 2 is true, and Statement 2 is the correct explanation for Statement 1.

To solve the problem, we need to analyze the two statements provided and determine their validity and relationship. ### Step-by-Step Solution: 1. **Understanding Statement 1**: - Statement 1 claims that when a body is dropped (let's call it Body A) and another body is thrown horizontally (let's call it Body B) from the same height, both bodies reach the ground at the same time. - This is true because the time taken for an object to fall solely depends on the height from which it is dropped and the acceleration due to gravity (g), not on the horizontal motion. ...
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