A ball is released from a height h. If t1 and t2 be the time required to complete first half and second half of the distance respectively. Then, choose the correct relation between t1 and t2.

Question

A ball is released from a height h. If t1 and t2 be the time required to complete first half and second half of the distance respectively. Then, choose the correct relation between t1 and t2. (A) t 1=(√2) t 2 (B) t 1=(√2-1) t 2 (C) t 2=(√2+1) t 1 (D) t 2=(√2-1) t 1

Tardigrade Admin · Accepted Answer

For first ( h /2) ( h /2)=(1/2) gt 12 For total height h h =(1/2) g ( t 1+ t 2)2 (1/√2)=( t 1/ t 1+ t 2) 1+( t 2/ t 1)=√2 ( t 1/ t 2)=(1/√2-1) t 2=(√2-1) t 1

Q. A ball is released from a height $h$ . If $t_{1}$ and $t_{2}$ be the time required to complete first half and second half of the distance respectively. Then, choose the correct relation between $t_{1}$ and $t_{2}$ .

$t_{1} = (2) t_{2}$

$t_{1} = (2 - 1) t_{2}$

$t_{2} = (2 + 1) t_{1}$

$t_{2} = (2 - 1) t_{1}$

For first $\frac{h}{2}$
$\frac{h}{2} = \frac{1}{2} g t_{1}^{2}$
For total height $h$
$h = \frac{1}{2} g (t_{1} + t_{2})^{2}$
$\frac{1}{2} = \frac{t _{1}}{t _{1} + t _{2}}$
$1 + \frac{t _{2}}{t _{1}} = 2$
$\frac{t _{1}}{t _{2}} = \frac{1}{2 - 1}$
$t_{2} = (2 - 1) t_{1}$

Q. A ball is released from a height h. If t1​ and t2​ be the time required to complete first half and second half of the distance respectively. Then, choose the correct relation between t1​ and t2​.

t1​=(2​)t2​

t1​=(2​−1)t2​

t2​=(2​+1)t1​

t2​=(2​−1)t1​