If-at-a-height-of-40-m-the-direction-of-motion-of-a-projectile-makes-an-angle-pi-4-with-the-horizontal-then-its-initial-velocity-and-angle-of-projection-are-respectively-a-30-1-2-cos-1-4-5

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Question Number 20316 by Tinkutara last updated on 25/Aug/17

$$\mathrm{If}\mathrm{at}\mathrm{a}\mathrm{height}\mathrm{of}40\mathrm{m},\mathrm{the}\mathrm{direction}\mathrm{of}$$$$\mathrm{motion}\mathrm{of}\mathrm{a}\mathrm{projectile}\mathrm{makes}\mathrm{an}\mathrm{angle}$$$$\pi /4\mathrm{with}\mathrm{the}\mathrm{horizontal},\mathrm{then}\mathrm{its}\mathrm{initial}$$$$\mathrm{velocity}\mathrm{and}\mathrm{angle}\mathrm{of}\mathrm{projection}\mathrm{are},$$$$\mathrm{respectively}$$$$\left(a\right)30,\frac{1}{2}{\cos }^{-1}(-\frac{4}{5})$$$$\left(b\right)30,\frac{1}{2}{\cos }^{-1}(-\frac{1}{2})$$$$\left(c\right)50,\frac{1}{2}{\cos }^{-1}(-\frac{8}{25})$$$$\left(d\right)60,\frac{1}{2}{\cos }^{-1}(-\frac{1}{4})$$

Commented by Tinkutara last updated on 25/Aug/17

$$\mathrm{I}\mathrm{think}\mathrm{velocity}\mathrm{of}\mathrm{projection}\mathrm{should}\mathrm{be}$$$$\mathrm{given}.{\mathrm{Isn}}^{\prime }\mathrm{t}\mathrm{it}?$$

Commented by ajfour last updated on 25/Aug/17

$$onemoreinformationneedbe$$$$given..$$

Commented by Tinkutara last updated on 25/Aug/17

$$\mathrm{This}\mathrm{is}\mathrm{the}\mathrm{wrong}\mathrm{solution}\mathrm{given}\mathrm{in}$$$$\mathrm{book}\mathrm{or}\mathrm{it}\mathrm{is}\mathrm{correct}?$$

Commented by Tinkutara last updated on 25/Aug/17

Commented by Joel577 last updated on 25/Aug/17

$$howdiditsay50m/s?$$

Commented by Tinkutara last updated on 25/Aug/17

$$\mathrm{Yes},\mathrm{so}\mathrm{this}\mathrm{solution}\mathrm{is}\mathrm{wrong}\mathrm{but}\mathrm{it}\mathrm{is}$$$$\mathrm{in}\mathrm{my}\mathrm{book}.$$

Commented by ajfour last updated on 25/Aug/17

$$-1⩽\cos 2\theta ⩽1$$$$-1⩽-\frac{2gh}{u^2}⩽1$$$$\Rightarrow u^2⩾2gh$$$$u^2⩾800$$$$u⩾20\sqrt{2}(\approx 28m/s).$$$$ifu=30m/s\Rightarrow \theta =\frac{1}{2}{\cos }^{-1}(-\frac{8}{9})$$$$ifu=40m/s\Rightarrow \theta =\frac{1}{2}{\cos }^{-1}(-\frac{1}{2})$$$$ifu=50m/s\Rightarrow \theta =\frac{1}{2}{\cos }^{-1}(-\frac{8}{25})$$$$ifu=60m/s\Rightarrow \theta =\frac{1}{2}{\cos }^{-1}(-\frac{2}{9})$$$$\left(c\right)isoneofthepossiblesolutions$$$$\left(a\right),\left(b\right),\left(d\right)arejustnotpossible.$$

Commented by Tinkutara last updated on 25/Aug/17

$$\mathrm{Thanks}\mathrm{you}\mathrm{very}\mathrm{much}\mathrm{Sir}!\mathrm{So}\mathrm{it}\mathrm{is}\mathrm{to}$$$$\mathrm{be}\mathrm{seen}\mathrm{by}\mathrm{the}\mathrm{options}.$$

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