Question

A bullet is fired 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

Answer: (C)

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 $(t)=\frac{\text{ Distance }}{\text{ Velocity }}$
$\therefore t=\frac{100}{1500}=\frac{1}{15}\sec$....(1)
The bullet performs vertical journey for this time.
For vertical journey, $h=ut+\frac{1}{2}g{t}^2$
$h=0+\frac{1}{2}\times 10\times {\left(\frac{1}{15}\right)}^2\text{ or, }h=\frac{20}{9}cm=2.2cm$