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(A) The formulas for range $R$ and maximum height $H$ are:$R = \frac{2 u_x u_y}{g}$ and $H = \frac{u_y^2}{2g}$.$(A)$ $u_x \rightarrow 2u_x, u_y \right

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$(A \rightarrow q, B \rightarrow q, r, C \rightarrow r, s, D \rightarrow s)$

Vedclass · Answer

(A) The formulas for range $R$ and maximum height $H$ are:$R = \frac{2 u_x u_y}{g}$ and $H = \frac{u_y^2}{2g}$.$(A)$ $u_x \rightarrow 2u_x, u_y \rightarrow u_y/2$: $R' = \frac{2(2u_x)(u_y/2)}{g} = R$. So, $A \rightarrow q$.$(B)$ $u_y \rightarrow 2u_y, u_x \rightarrow u_x/2$: $R' = \frac{2(u_x/2)(2u_y)}{g} = R$. Also, $H' = \frac{(2u_y)^2}{2g} = 4H$. So, $B \rightarrow q, s$.$(C)$ $u_x \rightarrow 2u_x, u_y \rightarrow 2u_y$: $R' = \frac{2(2u_x)(2u_y)}{g} = 4R$ $(r)$. $H' = \frac{(2u_y)^2}{2g} = 4H$ $(s)$. So, $C \rightarrow r, s$.$(D)$ $u_y \rightarrow 2u_y$: $H' = \frac{(2u_y)^2}{2g} = 4H$ $(s)$. So, $D \rightarrow s$.Matching: $A \rightarrow q$, $B \rightarrow q, s$, $C \rightarrow r, s$, $D \rightarrow s$. Option $(A)$ is the closest match given the provided choices.

Column $I$	Column $II$
$(A)$ $u_x$ is doubled, $u_y$ is halved	$(p)$ $H$ will remain unchanged
$(B)$ $u_y$ is doubled, $u_x$ is halved	$(q)$ $R$ will remain unchanged
$(C)$ $u_x$ and $u_y$ both are doubled	$(r)$ $R$ will become four times
$(D)$ Only $u_y$ is doubled	$(s)$ $H$ will become four times

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