Question

A projectile fired at an angle of ${45}^{\circ }$ travels a total distance $R$, called the range, which depends only on the initial speed $v$ and the acceleration of gravity $g$. Using dimensional analysis, find how $R$ depends on the speed and on $g$.

• A. $R\alpha \frac{v^2}{g}$
• B. $R\alpha \frac{v}{g^2}$
• C. $R\alpha \frac{g}{v^2}$
• D. None of these

Answer 1

The correct option is A $R\alpha \frac{v^2}{g}$

$R\alpha v^a{g}^b\Rightarrow \left[L\right]=\left[L{T}^{-1}{]}^a\right[L{T}^{-2}{]}^b$

$\Rightarrow a+b=1,-a-2b=0$

$\Rightarrow a=2,b=-1\Rightarrow R\alpha \frac{v^2}{g}$