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  4. A projectile is projected with initial velocity (6 hati+8 hatj) ms -1 If g=10 m s -2, then horizontal range is

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Q. A projectile is projected with initial velocity $(6 \hat{i}+8 \hat{j}) ms ^{-1}$ If $g=10 m s ^{-2}$, then horizontal range is

Motion in a Plane

Solution:

Here, $u \cos \theta=6, u \sin \theta=8$ and
$g=10 \,m \,s ^{-2}$
$\therefore R =\frac{u^{2} \sin 2 \theta}{g}=\frac{2 u^{2} \sin \theta \cos \theta}{g}=\frac{2(u \sin \theta)(u \cos \theta)}{g}$
$=\frac{2 \times 8 \times 6}{10}=9.6 \,m$