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Q.
A bullet is fired with a speed of $1500\, m / s$ in order to hit a target $100 \,m$ away. If $g=10\, m / s ^2$. The gun should be aimed
Motion in a Plane
Solution:
The bullet performs a horizontal journey of $100\, cm$ with constant velocity of $1500 \, m / s$. 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, $h = ut +\frac{1}{2} gt ^2$
$h =0+\frac{1}{2} \times 10 \times\left(\frac{1}{15}\right)^2 \text { or, } h =\frac{20}{9} cm =2.2 \, cm$