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A body is moving with an initial velocity of \(10 \sqrt{2} \mathrm{~ms}^{-1}\) in the north-east direction. If it is subjected to an acceleration of \(2 \mathrm{~ms}^{-2}\) directed towards the south, then velocity of the body after \(5 \mathrm{~s}\) is
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Verified Answer
The correct answer is:
\(10 \mathrm{~ms}^{-1}\), towards east
The given situation is shown in the following figure
Initial velocity of body,
\(\begin{aligned}
& \mathbf{u}=10 \sqrt{2} \cos 45^{\circ} \hat{\mathbf{i}}+10 \sqrt{2} \cos 45^{\circ} \hat{\mathbf{j}} \\
& =10 \hat{\mathbf{i}}+10 \hat{\mathbf{j}}=10(\hat{\mathbf{i}}+\hat{\mathbf{j}})
\end{aligned}\)
Acceleration applied on body in south direction,
\(\mathbf{a}_s=2(-\hat{\mathbf{j}})=-2 \hat{\mathbf{j}}\)
\(\therefore\) Velocity of body after \(5 \mathrm{~s}\) is given as
\(\begin{aligned}
\mathbf{v} & =\mathbf{u}+\mathbf{a}_s t=10(\hat{\mathbf{i}}+\hat{\mathbf{j}})+(-2 \hat{\mathbf{j}}) \times 5 \\
& =10 \hat{\mathbf{i}}+10 \hat{\mathbf{j}}-10 \hat{\mathbf{j}}=10 \hat{\mathbf{i}}
\end{aligned}\)
Hence, body will move towards east with the velocity \(10 \mathrm{~ms}^{-1}\).
Initial velocity of body,
\(\begin{aligned}
& \mathbf{u}=10 \sqrt{2} \cos 45^{\circ} \hat{\mathbf{i}}+10 \sqrt{2} \cos 45^{\circ} \hat{\mathbf{j}} \\
& =10 \hat{\mathbf{i}}+10 \hat{\mathbf{j}}=10(\hat{\mathbf{i}}+\hat{\mathbf{j}})
\end{aligned}\)
Acceleration applied on body in south direction,
\(\mathbf{a}_s=2(-\hat{\mathbf{j}})=-2 \hat{\mathbf{j}}\)
\(\therefore\) Velocity of body after \(5 \mathrm{~s}\) is given as
\(\begin{aligned}
\mathbf{v} & =\mathbf{u}+\mathbf{a}_s t=10(\hat{\mathbf{i}}+\hat{\mathbf{j}})+(-2 \hat{\mathbf{j}}) \times 5 \\
& =10 \hat{\mathbf{i}}+10 \hat{\mathbf{j}}-10 \hat{\mathbf{j}}=10 \hat{\mathbf{i}}
\end{aligned}\)
Hence, body will move towards east with the velocity \(10 \mathrm{~ms}^{-1}\).
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