From the top of a tower a stone is thrown up and reaches the ground in time t1 = 9s. A second stone is thrown down with the same speed and reaches the ground in time t2 = 4s. A third stone is released from rest and reaches the ground in time t3, which is equal to

Question

From the top of a tower a stone is thrown up and reaches the ground in time t1 = 9s. A second stone is thrown down with the same speed and reaches the ground in time t2 = 4s. A third stone is released from rest and reaches the ground in time t3, which is equal to (A) 6.5 s (B) 6 s (C) (5/36)s (D) 65 s

Tardigrade Admin · Accepted Answer

Taking downward motion of the first stone from A to ground, we have

h = - u t_{1} + \frac{1}{2} g t_{1}^{2}

.....(i)
Taking downward motion of second stone from A to ground, we have

h - u t_{2} + \frac{1}{2} g t_{2}^{2}

....(ii)
Third stone

h = \frac{1}{2} g t_{3}^{2}

.....(iii)
Multiplying Eq. (i) by

t_{2}

and Eq. (ii) by

t_{1}

and adding, we get

h (t_{1} + t_{2}) = \frac{1}{2} g t_{1} t_{2} (t_{1} + t_{2})

\Rightarrow h = \frac{1}{2} g t_{1} t_{2}

.......(iv)
From Eqs. (iii) and (iv),

t_{3}^{2} = t_{1} t_{2}

or

t_{3} t_{1} t_{2}

= 9 \times 4 = 6 s

Q. From the top of a tower a stone is thrown up and reaches the ground in time $t_{1}$ = 9s. A second stone is thrown down with the same speed and reaches the ground in time $t_{2}$ = 4s. A third stone is released from rest and reaches the ground in time $t_{3}$ , which is equal to

6.5 s

6 s

$\frac{5}{36} s$

65 s

Q. From the top of a tower a stone is thrown up and reaches the ground in time t1​ = 9s. A second stone is thrown down with the same speed and reaches the ground in time t2​ = 4s. A third stone is released from rest and reaches the ground in time t3​, which is equal to

6.5 s

6 s

365​s

65 s

Q. From the top of a tower a stone is thrown up and reaches the ground in time $t_{1}$ = 9s. A second stone is thrown down with the same speed and reaches the ground in time $t_{2}$ = 4s. A third stone is released from rest and reaches the ground in time $t_{3}$ , which is equal to

$\frac{5}{36} s$