At a given instant of time two particles are having the position vectors $4 \hat{\mathbf{i}}+4 \hat{\mathbf{j}}+57 \hat{\mathbf{k}}$ metres and $2 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}+5 \hat{\mathbf{k}}$ respectively. If the velocity of the first particle be $0.4 \hat{\mathbf{i}} \mathrm{ms}^{-1}$,…

Question

At a given instant of time two particles are having the position vectors $4 \hat{\mathbf{i}}+4 \hat{\mathbf{j}}+57 \hat{\mathbf{k}}$ metres and $2 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}+5 \hat{\mathbf{k}}$ respectively. If the velocity of the first particle be $0.4 \hat{\mathbf{i}} \mathrm{ms}^{-1}$, the velocity of second particle in metre per second if they collide after $10 \mathrm{sec}$ is

Aicharya · Accepted Answer

$\begin{aligned} s_1+\left(u_1ight) t & =s_2+\left(u_2ight) t \ & =(4 \hat{\mathbf{i}}-4 \hat{\mathbf{j}}+7 \hat{\mathbf{k}})+(0.4 \hat{\mathbf{i}}) 10 \ & =(2 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}+5 \hat{\mathbf{k}})+\left(u_2ight) 10 \ \Rightarrow \quad u_2 & =\frac{(6 \hat{\mathbf{i}}-6 \hat{\mathbf{j}}+2 \hat{\mathbf{k}})}{10} \ & =0.6\left[\hat{\mathbf{i}}-\hat{\mathbf{j}}+\frac{1}{3} \hat{\mathbf{k}}ight]\end{aligned}$

At a given instant of time two particles are having the position vectors $4 \hat{\mathbf{i}}+4…

Solution