Question

A particle is thrown vertically up with speed $u$ so that distance covered in last second of flight is $35m$. If $g=10m/s^2$ then initial speed of throw is

• A. $20m/s$
• B. $30m/s$
• C. $40m/s$
• D. $50m/s$

Answer 1

The correct option is C $40m/s$

Particle is thrown vertically up with speed $um/s$ distance covered in last second of flight is $35m$.

$\to$ time taken to reach the maximum height, $t=\frac{u}{g}$ sec particle $35m$ in last time at flight means it covers $35m$ before striking the ground.

$\to$ initial velocity=velocity at max height =0

Distance travelled in nth second:-

$S_n=u^{\prime }+\frac{1}{2}g(2n-1)$

$Sn=35,g=10m{s}^{-2},n=t=u/g$, initial velocity $u^{\prime }=0$

$-35=\frac{1}{2}\times -10\times [\frac{2u}{g}-1]$

$35=10\times \frac{u}{10}-5$

$40=u$

$u=40m/s$