A body is dropped from a height h. If t1 and t2 be the times in covering first half and the next half distances respectively, then the relation between t1 and t2 is

Question

A body is dropped from a height h. If t1 and t2 be the times in covering first half and the next half distances respectively, then the relation between t1 and t2 is (A) t1 = t2 (B) t1 = 2t2 (C) t1 = 3t2 (D) t1 = (t2/(√2 - 1))

Tardigrade Admin · Accepted Answer

t1 = √(2(h/2)/g) = √(h/g) ⇒ t1+t2 = √(2h/g) ⇒ t2 =√(2h/g) -t1 = (√2 -1)√(h/g) ⇒ (t1/t2) = (1/√2-1) ⇒ (t2/√2-1)

Q. A body is dropped from a height $h$ . If $t_{1}$ and $t_{2}$ be the times in covering first half and the next half distances respectively, then the relation between $t_{1}$ and $t_{2}$ is

$t_{1} = t_{2}$

$t_{1} = 2 t_{2}$

$t_{1} = 3 t_{2}$

$t_{1} = \frac{t _{2}}{( 2 - 1 )}$

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

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

$\Rightarrow t_{2} = \frac{2 h}{g} - t_{1} = (2 - 1) \frac{h}{g}$

$\Rightarrow \frac{t _{1}}{t _{2}} = \frac{1}{2 - 1}$

$\Rightarrow \frac{t _{2}}{2 - 1}$

Q. A body is dropped from a height h. If t1​ and t2​ be the times in covering first half and the next half distances respectively, then the relation between t1​ and t2​ is

t1​=t2​

t1​=2t2​

t1​=3t2​

t1​=(2​−1)t2​​