A body of mass 2 kg moving with velocity of $\overrightarrow{\mathrm{v}}_{\mathrm{in}}=3 \hat{\mathrm{i}}+4…

A body of mass 2 kg moving with velocity of $\overrightarrow{\mathrm{v}}_{\mathrm{in}}=3 \hat{\mathrm{i}}+4 \hat{\mathrm{j}} \mathrm{ms}^{-1}$ enters into a constant force field of 6 N directed along positive z -axis. If the body remains in the field for a period of $\frac{5}{3}$ seconds, then velocity of the body when it emerges from force field is
  1. $4 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}+5 \hat{\mathrm{k}}$
  2. $3 \hat{\mathrm{i}}+4 \hat{\mathrm{j}}+5 \hat{\mathrm{k}}$
  3. $3 \hat{i}+4 \hat{j}-5 \hat{k}$
  4. $3 \hat{\mathrm{i}}+4 \hat{\mathrm{j}}+\sqrt{5} \hat{\mathrm{k}}$

Solution

$\begin{aligned} & \overrightarrow{\mathrm{a}}=\frac{\mathrm{B}}{2} \hat{\mathrm{k}}=3 \hat{\mathrm{k}}, \mathrm{t}=\frac{5}{3} \mathrm{~s} \\ & \overrightarrow{\mathrm{u}}=3 \hat{\mathrm{i}}+4 \hat{\mathrm{j}} \\ & \overrightarrow{\mathrm{v}}=\overrightarrow{\mathrm{u}}+\overrightarrow{\mathrm{a}} \mathrm{t}=3 \hat{\mathrm{i}}+4 \hat{\mathrm{j}}+5 \hat{\mathrm{k}}\end{aligned}$

Asked in: JEE Main 2025 (08 Apr Shift 2)

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