Answer :
Answer:
[tex]R_{max} = 2.125 R[/tex]
Explanation:
If the maximum height attained by the rock is equal to the range of the rock
then we will say
[tex]H = R[/tex]
[tex]\frac{v^2 sin^2\theta}{2g} = \frac{v^2 sin(2\theta)}{g}[/tex]
so from this we can say
[tex]\frac{sin^2\theta}{2} = 2sin\theta cos\theta[/tex]
[tex]tan\theta = 4[/tex]
[tex]\theta = 75.96 degree[/tex]
now original range is given as
[tex]R = \frac{v^2 sin(2\theta)}{g}[/tex]
[tex]R = \frac{v^2 sin(2\times 75.96)}{g}[/tex]
[tex]R = 0.47\frac{v^2}{g}[/tex]
now we know that for maximum possible range we need to throw at 45 degree
[tex]R_{max} = \frac{v^2 sin(2\times 45)}{g}[/tex]
[tex]R_{max} = \frac{v^2}{g}[/tex]
[tex]R_{max} = 2.125 R[/tex]