Question

A ball is thrown up under gravity $(g=10m/se{c}^2)$. Find its velocity after 1.0 sec at a height of 10 m

• A. $5m/se{c}^2$
• B. $5m/sec$
• C. $10m/sec$
• D. $15m/sec$

Answer 1

The correct option is B $5m/sec$

suppose velocity of projection $=u$

then velocity at height $h$ will be

$v=\sqrt{u^2-2gh}$

putting $h=10m,g=10m/s^2$

we get

$v=\sqrt{u^2-200}...\left(1\right)$

but at $t=1$ second is the time taken to reduce $u$ to $v$

so $v=u-g\left(1\right)=u-g$

$u=v+g$

putting this in equation 1

$v^2=u^2-200={(v+g)}^2-200$

or $v^2=v^2+g^2+2vg-200$

$\Rightarrow$ $0=100+2v\left(10\right)-200$

$0=-100+20v$

$v=5m/s$