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  4. A coastguard ship locates a pirate ship at a distance 560 m. It fires a cannon ball with an initial speed 82 ms-1 . At what angle from horizontal the ball must be fired so that it hits the pirate ship?

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Q. A coastguard ship locates a pirate ship at a distance $560 \,m$. It fires a cannon ball with an initial speed $82 \, ms^{-1} $ . At what angle from horizontal the ball must be fired so that it hits the pirate ship?

Delhi UMET/DPMTDelhi UMET/DPMT 2009

Solution:

Range $=\frac{u^{2} \sin 2 \theta}{g}$
$ \therefore 560=\frac{(82)^{2} \sin 2 \theta}{10}$
or $\sin 2 \theta=0.832\left[\sin 56.30^{\circ}=0.832\right]$
$ \Rightarrow \theta \approx 27^{\circ}$