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Question Number 15407 by Tinkutara last updated on 10/Jun/17

$$\mathrm{A}\mathrm{ball}\mathrm{is}\mathrm{thrown}\mathrm{vertically}\mathrm{upward}$$$$\mathrm{with}\mathrm{velocity}20\mathrm{m}/\mathrm{s}\mathrm{from}\mathrm{a}\mathrm{rail}\mathrm{road}$$$$\mathrm{car}\mathrm{moving}\mathrm{with}\mathrm{a}\mathrm{velocity}5\mathrm{m}/\mathrm{s}$$$$\mathrm{horizontally}.\mathrm{A}\mathrm{person}\mathrm{standing}\mathrm{on}\mathrm{the}$$$$\mathrm{ground}\mathrm{observes}\mathrm{its}\mathrm{motion}\mathrm{as}\mathrm{projectile}.$$$$\mathrm{Find}\mathrm{maximum}\mathrm{height}\mathrm{attained}\mathrm{by}\mathrm{the}$$$$\mathrm{ball}\mathrm{if}\mathrm{point}\mathrm{of}\mathrm{projection}\mathrm{is}\mathrm{at}\mathrm{a}\mathrm{height}$$$$3\mathrm{m}\mathrm{from}\mathrm{the}\mathrm{ground}.$$

Answered by mrW1 last updated on 10/Jun/17

$$\mathrm{y}=3+20\mathrm{t}-\frac{1}{2}\times {10\mathrm{t}}^2=3+20\mathrm{t}-{5\mathrm{t}}^2$$$$=23-5({\mathrm{t}}^2-4\mathrm{t}+4)=23-5{(\mathrm{t}-2)}^2⩽23$$$$\Rightarrow \max .\mathrm{height}=23\mathrm{m}$$

Commented by Tinkutara last updated on 10/Jun/17

$$\mathrm{Thanks}\mathrm{Sir}!$$

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