A body of mass \(10 kg\) is projected at an angle of \(45^{\circ}\) with the horizontal. The trajectory of the body is observed to pass through a point \((20,10)\). If \(T\) is the time of flight, then its momentum vector, at time \(t =\frac{ T }{\sqrt{2}}\), is. \(\left[\right.\) Take \(\left.g=10 m / s ^{2}\right]\)

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Answer & Solution

Correct Answer

(D) \(100 \sqrt{2} \hat{i}+(100 \sqrt{2}-200) \hat{j}\)

Detailed explanation

\(y = x -\frac{10 x ^{2}}{2 u ^{2}\left(\frac{1}{2}\right)} \Rightarrow 10=20-\frac{(10)(100)}{ u ^{2}}\)

\(u=20\)

\(T=\frac{(2)(20)}{\sqrt{2}(10)}=2 \sqrt{2}\)

\(\overrightarrow{ v }=10 \sqrt{2} \hat{ i }+(10 \sqrt{2}-10(2)] \hat{ j }\)

Momentum \(\vec{p}=M \vec{v}=100 \sqrt{2} \hat{i}+(100 \sqrt{2}-200) \hat{j}\)

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List\(-I\)	List\(-II\)
\((a)\) \({R}_{{H}}\) (Rydberg constant)	\((i)\) \({kg} {m}^{-1} {s}^{-1}\)
\((b)\) \(h\) (Planck's constant)	\((ii)\) \({kg} {m}^{2} {s}^{-1}\)
\((c)\) \(\mu_{{B}}\) (Magnetic field energy density)	\((iii)\) \({m}^{-1}\)
\((d)\) \(\eta\) (coefficient of viscocity)	\((iv)\) \({kg} {m}^{-1} {s}^{-2}\)