At t = 0, two particles B and C are located at the origin of the coordinate system. Then they start moving simultaneously. B moves under constant acceleration of 2k^ m/s2 with an initial velocity of 8j^ m/s. Particle C moves with constant velocity V→0 in such a way that B and C collide at t = 4 s. Then mark the INCORRECT statement(s).

Particle B:vB=uB+aBtV→B=8j^+2tk^ r→B=uBt+12aBt2=8tj^+122t2k^=8tj^+t2k^Particle C:r→C=Vxti^+Vytj^+Vztk^V→C=V→0=Vxi^+Vyj^+Vzk^ At t=4sr→B=r→C 8tj^+t2k^ =Vxti^+Vytj^+Vztk^On comparing we get⇒Vx=0,Vy=8,Vz=t=4∴V→0=8j^+4k^Position vector of collision r→B=84j^+42k^=32j^+16k^

At t = 0, two particles B and C are located at the origin of the coordinate system. Then they start moving simultaneously. B moves under constant acceleration of 2k^ m/s2 with an initial velocity of 8j^ m/s. Particle C moves with constant velocity V→0 in such a way that B and C collide at t = 4 s. Then mark the INCORRECT statement(s).

Particle B:vB=uB+aBtV→B=8j^+2tk^ r→B=uBt+12aBt2=8tj^+122t2k^=8tj^+t2k^Particle C:r→C=Vxti^+Vytj^+Vztk^V→C=V→0=Vxi^+Vyj^+Vzk^ At t=4sr→B=r→C 8tj^+t2k^ =Vxti^+Vytj^+Vztk^On comparing we get⇒Vx=0,Vy=8,Vz=t=4∴V→0=8j^+4k^Position vector of collision r→B=84j^+42k^=32j^+16k^

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At t = 0, two particles B and C are located at the origin of the coordinate system. Then they start moving simultaneously. B moves under constant acceleration of $2 \hat{k} m / s^{2}$ with an initial velocity of $8 \hat{j} m / s$ . Particle C moves with constant velocity ${\vec{V}}_{0}$ in such a way that B and C collide at t = 4 s. Then mark the INCORRECT statement(s).

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It is not possible that B and C collide with each other for any value of ${\vec{v}}_{0}$

${\vec{V}}_{0} = (8 \hat{j} + 4 \hat{k})$ m/s

Position vector of location where two particles collide is $(16 \hat{i} + 32 \hat{k}) m$

$\vec{V_{0}} = 4 \vec{j} + 8 \vec{k}$

answer is B, C, D.

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Detailed Solution

$\begin{array}{l} P a r t i c l e B : \\ v_{B} = u_{B} + a_{B} t \\ {\vec{V}}_{B} = 8 \hat{j} + 2 t \hat{k} \end{array}$

$\begin{array}{l} {\vec{r}}_{B} = u_{B} t + \frac{1}{2} a_{B} t^{2} = 8 t \hat{j} + \frac{1}{2} (2) t^{2} \hat{k} \\ = 8 t \hat{j} + {(t)}^{2} \hat{k} \\ P a r t i c l e C : \\ {\vec{r}}_{C} = V_{x} t \hat{i} + V_{y} \hat{tj} + V_{z} t \hat{k} \\ {\vec{V}}_{C} = {\vec{V}}_{0} = V_{x} \hat{i} + V_{y} \hat{j} + V_{z} \hat{k} \end{array}$

$\begin{array}{l} At t = 4 s \\ {\vec{r}}_{B} = {\vec{r}}_{C} \\ \begin{array}{l} 8 t \hat{j} + {(t)}^{2} \hat{k} \end{array} = V_{x} t \hat{i} + V_{y} \hat{tj} + V_{z} t \hat{k} \end{array}$

$\begin{array}{l} O n c o m p a r i n g w e g e t \\ \Rightarrow V_{x} = 0, V_{y} = 8, V_{z} = t = 4 \\ ∴ {\vec{V}}_{0} = 8 \hat{j} + 4 \hat{k} \end{array}$