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

Question

Aicharya · Accepted Answer

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 $10 \mathrm{~ms}^{-1}$.

A body is moving with an initial velocity of \(10 \sqrt{2} \mathrm{~ms}^{-1}\) in the north-east direction.…

Solution