Question 122: Motion in 1D

Question

From the top of a tower, a ball is thrown vertically upward which reaches the ground in 6 s. A second ball thrown vertically downward from the same position with the same speed reaches the ground in 1.5 s. A third ball released, from the rest from the same location, will reach the ground in ____________ s.

Accepted Answer

Based on the situation
$$h =  - u{t_1} + {1 \over 2}gt_1^2$$ $$	o$$ throwing up ....... (i)
$$h = u{t_2} + {1 \over 2}gt_2^2$$ $$	o$$ throwing up ....... (ii)
$$h = {1 \over 2}g{t^2}$$ $$	o$$ dropping .......... (iii)
and $$0 = u({t_1} - {t_2}) - {1 \over 2}g{({t_1} - {t_2})^2}$$ ....... (iv)
solving above equations
$$t = \sqrt {{t_1}{t_2}} $$
$$ \Rightarrow t = \sqrt {6 	imes 1.5}  = 3\,s$$

Motion in 1D

Integer / Numeric Answer Type