Question

A body projected upward is at the same height from the ground at t=3s and t=7s. Find the maximum height attained by it $\left[g=10m/s^2\right]$.

• A. $25m$
• B. $100m$
• C. $125m$
• D. $150m$

Answer 1

The correct option is C $125m$

$t_{!}=3$ , $t_2=7$

using 2nd equation of motion in vertical direction :

$s_y=u_{y}t-\frac{g{t}^2}{2}$

$g{t}^2-2u_{y}t+2s_y=0$

for a given $s_y$ there are 2 value of time satisfying the equation

therefore $t_1,t_2$ are roots of this equation

using sum of roots $=\frac{-b}{a}$

$t_1+t_2=\frac{2u_y}{g}$

$10=\frac{2usin\theta }{g}=T$, where T is time of flight

using relation between$T$and$H$

$H=\frac{g{T}^2}{8}$

$H=\frac{10\times 100}{8}$

$H=125m$