269989 A body is projected up such that its position vector varies with time as \(\vec{r}=\left\{3 t \hat{i}+\left(4 t-5 t^{2}\right) \hat{j}\right\}\) m. Here \(\boldsymbol{t}\) is in second. The time when its \(y\)-coordinate is zero is

269990 The position of a particle is given by \(\vec{r}=3 t \hat{i}-2 t^{2} \hat{j}+4 \hat{k}\) m where \(t\) is in second and the co-efficients have proper units for \(r\) to be in \(\mathrm{m}\). The magnitude and direction of velocity of the particle at \(t=2 \mathrm{~s}\) is

269991 A particle starts from origin at \(t=0\) with a constant velocity \(5 \hat{i} \mathrm{~ms}^{-1}\) and moves in \(\mathbf{x y}\) plane under action of a force which produces a constant acceleration of \((3 \hat{i}+2 \hat{j}) \mathrm{ms}^{-2}\). The \(\mathbf{y}\) - coordinate of the particle at the instant its \(x\) co-ordinate is \(84 \mathrm{~m}\) in $\mathbf{m}$ is

269988 Two particles having position vectors ${\overrightarrow{r}}_1=(3\overrightarrow{i}+5\overrightarrow{j})m$ and $\overrightarrow{r_2}=(-5\overrightarrow{i}+3\overrightarrow{j})m$ are moving with velocities $\overrightarrow{V_1}=(4\hat{i}-4\hat{j}){\mathrm{ms}}^{-1}$ and $\overrightarrow{V_2}=(a\hat{i}-3\hat{j}){\mathrm{ms}}^{-1}$. If they collide after 2 seconds, the value of ' $a$ ' is

269989 A body is projected up such that its position vector varies with time as $\overrightarrow{r}=\{3t\hat{i}+(4t-5t^2)\hat{j}\}$ m. Here $\text{boldsymbol}t$ is in second. The time when its $y$-coordinate is zero is

269990 The position of a particle is given by $\overrightarrow{r}=3t\hat{i}-2t^2\hat{j}+4\hat{k}$ m where $t$ is in second and the co-efficients have proper units for $r$ to be in $\mathrm{m}$. The magnitude and direction of velocity of the particle at $t=2\mathrm{s}$ is

269991 A particle starts from origin at $t=0$ with a constant velocity $5\hat{i}{\mathrm{ms}}^{-1}$ and moves in $\mathbf{x}\mathbf{y}$ plane under action of a force which produces a constant acceleration of $(3\hat{i}+2\hat{j}){\mathrm{ms}}^{-2}$. The $\mathbf{y}$ - coordinate of the particle at the instant its $x$ co-ordinate is $84\mathrm{m}$ in $\mathbf{m}$ is

269988 Two particles having position vectors ${\overrightarrow{r}}_1=(3\overrightarrow{i}+5\overrightarrow{j})m$ and $\overrightarrow{r_2}=(-5\overrightarrow{i}+3\overrightarrow{j})m$ are moving with velocities $\overrightarrow{V_1}=(4\hat{i}-4\hat{j}){\mathrm{ms}}^{-1}$ and $\overrightarrow{V_2}=(a\hat{i}-3\hat{j}){\mathrm{ms}}^{-1}$. If they collide after 2 seconds, the value of ' $a$ ' is

269989 A body is projected up such that its position vector varies with time as $\overrightarrow{r}=\{3t\hat{i}+(4t-5t^2)\hat{j}\}$ m. Here $\text{boldsymbol}t$ is in second. The time when its $y$-coordinate is zero is

269990 The position of a particle is given by $\overrightarrow{r}=3t\hat{i}-2t^2\hat{j}+4\hat{k}$ m where $t$ is in second and the co-efficients have proper units for $r$ to be in $\mathrm{m}$. The magnitude and direction of velocity of the particle at $t=2\mathrm{s}$ is

269991 A particle starts from origin at $t=0$ with a constant velocity $5\hat{i}{\mathrm{ms}}^{-1}$ and moves in $\mathbf{x}\mathbf{y}$ plane under action of a force which produces a constant acceleration of $(3\hat{i}+2\hat{j}){\mathrm{ms}}^{-2}$. The $\mathbf{y}$ - coordinate of the particle at the instant its $x$ co-ordinate is $84\mathrm{m}$ in $\mathbf{m}$ is

269988 Two particles having position vectors ${\overrightarrow{r}}_1=(3\overrightarrow{i}+5\overrightarrow{j})m$ and $\overrightarrow{r_2}=(-5\overrightarrow{i}+3\overrightarrow{j})m$ are moving with velocities $\overrightarrow{V_1}=(4\hat{i}-4\hat{j}){\mathrm{ms}}^{-1}$ and $\overrightarrow{V_2}=(a\hat{i}-3\hat{j}){\mathrm{ms}}^{-1}$. If they collide after 2 seconds, the value of ' $a$ ' is

269989 A body is projected up such that its position vector varies with time as $\overrightarrow{r}=\{3t\hat{i}+(4t-5t^2)\hat{j}\}$ m. Here $\text{boldsymbol}t$ is in second. The time when its $y$-coordinate is zero is

269990 The position of a particle is given by $\overrightarrow{r}=3t\hat{i}-2t^2\hat{j}+4\hat{k}$ m where $t$ is in second and the co-efficients have proper units for $r$ to be in $\mathrm{m}$. The magnitude and direction of velocity of the particle at $t=2\mathrm{s}$ is

269991 A particle starts from origin at $t=0$ with a constant velocity $5\hat{i}{\mathrm{ms}}^{-1}$ and moves in $\mathbf{x}\mathbf{y}$ plane under action of a force which produces a constant acceleration of $(3\hat{i}+2\hat{j}){\mathrm{ms}}^{-2}$. The $\mathbf{y}$ - coordinate of the particle at the instant its $x$ co-ordinate is $84\mathrm{m}$ in $\mathbf{m}$ is