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If the horizontal range of projectile be...

If the horizontal range of projectile be (a) and the maximum height attained by it is (b) then prove that the velocity of projection is
` [ 2 g (b+ a^2 /(16 b)) ] ^(1//2)`.

Text Solution

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Horizontal range, `(2v_(x_(0))v_(y0))/(g) =a.........(1)`
and maximum height, `(v_(y0)^(2))/(2g)=b ........(ii)`
From equation (ii), `v_(y0)^(2) =2gb .......(iii)`
and from equation (i) `v_(x0) =(ga)/(2v_(y_(0))`
`or v_(x0)^(2)=(g^(2)a^(2))/(4v_(y0)^(2)......(iv)`
Clearly, from equation (iii) and (iv),
`v_(x_(0))^(2)=(g^(2)a^(2))/(8 gb)=(ga^(2))/(8b) ......(v)`
If `v_(0)` is the velocity of projection, `v_(0)=sqrt(v_(xo)^(2)+v_(y0)^(2))=sqrt((ga^(2))/(8b)+2gb) or v_(0) =sqrt(2g(b+a^(2)//16)`
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