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  4. An object is projected at an angle of 45° with the horizontal. The horizontal range and maximum height reached will be in the ratio:

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Q. An object is projected at an angle of $ 45{}^\circ $ with the horizontal. The horizontal range and maximum height reached will be in the ratio:

KEAMKEAM 2005

Solution:

Horizontal range, $ R=\frac{{{u}^{2}}\sin 2\times 45}{g} $
$ =\frac{{{u}^{2}}}{g} $
Maximum height, $ h=\frac{{{u}^{2}}{{\sin }^{2}}45}{2g} $
$ =\frac{{{u}^{2}}}{4g} $
$ \frac{R}{h}=\frac{4}{1} $