Questions: Two identical stones are dropped from the rest. Stone A from height h, and stone B from height 2h. If stone A takes time (t) to reach the ground, then what time is taken by stone B to reach the ground? a) 4t b) 2t c) √2t d) t / √2 e) t / 2

Two identical stones are dropped from the rest. Stone A from height h, and stone B from height 2h. If stone A takes time (t) to reach the ground, then what time is taken by stone B to reach the ground?
a) 4t
b) 2t
c) √2t
d) t / √2
e) t / 2

Transcript text: 6. Two identical stones are dropped from the rest. Stone A from height h , and stone B from height 2 h . If stone A takes time $(t)$ to reach the ground, then what time is taken by stone B to reach the ground? a) $4 t$ b) $2 t$ c) $\sqrt{2} t$ d) $t / \sqrt{2}$ e) $t / 2$

Solution

Solution Steps

Step 1: Determine the time taken by stone A to reach the ground

Stone A is dropped from height $ h $. The time $ t $ it takes to reach the ground can be found using the equation of motion under gravity: \[ h = \frac{1}{2} g t^2 \] Solving for $ t $: \[ t = \sqrt{\frac{2h}{g}} \]

Step 2: Determine the time taken by stone B to reach the ground

Stone B is dropped from height $ 2h $. The time $ t_B $ it takes to reach the ground can be found using the same equation of motion under gravity: \[ 2h = \frac{1}{2} g t_B^2 \] Solving for $ t_B $: \[ t_B = \sqrt{\frac{4h}{g}} \] \[ t_B = 2 \sqrt{\frac{h}{g}} \]

Step 3: Relate the time taken by stone B to the time taken by stone A

We know from Step 1 that $ t = \sqrt{\frac{2h}{g}} $. To express $ t_B $ in terms of $ t $: \[ t_B = 2 \sqrt{\frac{h}{g}} \] \[ t = \sqrt{\frac{2h}{g}} \] \[ t_B = \sqrt{2} t \]

Final Answer

\[ \boxed{\sqrt{2} t} \]

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