Question

A bullet is fired horizontally with a speed of $1500m/s$ in order to hit a target $100m$ away. If $g=10m/s^2$. The gun should be aimed

• A. $15cm$ above the target
• B. $10cm$ above the target
• C. $2.2cm$ above the target
• D. directly towards the target

Answer 1

The correct option is C $2.2cm$ above the target

The bullet performs a horizontal journey of $100cm$ with constant velocity of $1500m/s$. The bullet also performs a vertical journey of h with zero initial velocity and downward acceleration $g$
Therefore for horizontal journey, time $t=\frac{Distance}{velocity}$
$t=\frac{100}{1500}=\frac{1}{15}sec........\left(1\right)$

The bullet performs vertical journey for this time
For vertical journey , $h=ut+\frac{1}{2}g{t}^2$

$h=0+\frac{1}{2}\times 10\times (\frac{1}{15}{)}^2$

$h=\frac{10}{2\times 15\times 15}m=\frac{10\times 100}{2\times 15\times 15}cm$

$h=2.2cm$
The gun should be aimed $\frac{20}{9}$ cm above the target