Question

An aeroplane is flying horizontally with a velocity of $600\text{km/hr}$ and at a height of $2,000\text{m}$. When it is vertically above a point $A$ on the ground, a bomb is released from it. The bomb strikes the ground at point $B$. The distance $AB$ (in kilometer) is (neglecting air resistance, take
$g=10{\text{m/s}}^2$ )

Answer 1

Taking downward direction as positive,
Using, $s_y=u_y+\frac{1}{2}{a}_y{t}^2$
$h=0+\frac{1}{2}g{t}^2$
$\Rightarrow t=\sqrt{\frac{2h}{g}}=\sqrt{\frac{2\times 2000}{10}}=20s$
Now,
$AB=s_x=u_{x}t+\frac{1}{2}{a}_x{t}^2$
$\Rightarrow s_x=(600\times \frac{5}{18})20+0$
$(\because a_x=0)$
$\Rightarrow s_x=3333.33\text{m}$
$=3.33\text{km}$