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  4. A projectile is fired at an angle 30° to the horizontal such that the vertical component of its initial velocity is 80 m/s. Find approximately the velocity of the projectile at time T/4 where T is time of flight.

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Q. A projectile is fired at an angle $30^{\circ}$ to the horizontal such that the vertical component of its initial velocity is $80 \,m/s$. Find approximately the velocity of the projectile at time $T/4$ where T is time of flight.

Motion in a Plane

Solution:

$u\, \sin\, 30^{0} =80 $
$\Rightarrow u=160\, m/s$
$u_{x} =u\,\,cos\,\,30^{\circ} =160 \frac{\sqrt{3}}{2} =80\sqrt{3} \,m/s$
$T=\frac {2u\,\,sin\,\,30^{\circ}}{g} =\frac{2 \times 80}{10} =16\, s$
$v_{y} =u_{y} -g \frac{T}{4} =80 -\frac{10\times16}{4}=40 \,m/s$
$v=\sqrt{v^{2}_{x}+v^{2}_{y}}$
$ =\sqrt{(80\sqrt{3})^{2} +40^{2}} =145 \,m/s$