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A stone is thrown up from the top of a t...

A stone is thrown up from the top of a tower and it takes time `t_(1)` to reach the ground. A second stone is thrown down with the same speed and it takes time `t_(2)` to reach the ground . How much time a third stone would take to reach the ground, if it is dropped down?

Text Solution

AI Generated Solution

To solve the problem step by step, we will analyze the motion of the three stones thrown from the top of a tower. ### Step 1: Understand the Problem We have three cases: 1. A stone is thrown upwards with an initial speed \( u \) and takes time \( t_1 \) to reach the ground. 2. A second stone is thrown downwards with the same initial speed \( u \) and takes time \( t_2 \) to reach the ground. 3. A third stone is simply dropped (initial speed \( u = 0 \)), and we need to find the time \( t \) it takes to reach the ground. ...
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Knowledge Check

  • A stone is thrown upwards from the top of a tower with some initial speed and it reaches the ground in 16 seconds. Now it is thrown with the same initial speed downward and it reaches the ground in 9 sec . In how much time will it reach the ground if the stone is allowed to fall freely under gravity from the same place ?

    A
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    B
    12.5 s
    C
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    D
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    A
    ` t_3=(1)/(2) (t_1+t_2) `
    B
    ` t_s=sqrt(t_1t_2) `
    C
    ` (1)/(t_3) = (1)/( t_2) -(1)/( t_1) `
    D
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    A
    6.5 s
    B
    6.0 s
    C
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    D
    none

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