JEE Mains · Physics · STD 11 - 3.2 motion in plane

Ship \(A\) is sailing towards north -east with velocity \(\vec v = 30\,\hat i + 50\hat j\,km/hr\) where \(\hat i\) points east and \(\hat j\) , north. Ship \(B\) is at a distance of \(80\, km\) east and \(150\, km\) north of Ship \(A\) and is sailing towards west at \(10\, km/hr\). \(A\) will be at minimum distance from \(B\) is.........\(hrs\)

A \(2.2\)
B \(4.2\)
C \(2.6\)
D \(3.2\)

Verified Solution

Answer & Solution

Correct Answer

(C) \(2.6\)

Step-by-step Solution

Detailed explanation

\begin{array}{l} if\,we\,take\,the\,position\,of\,ship\,'A'\,as\,\\ origin\,then\,positions\,velocity\,of\,both\\ ships\,can\,be\,given\,as:\\ {{\vec v}_A} = \left( {30\hat i + 50\hat j} \right)km/hr\\ {{\vec v}_B} = - 10\hat i\,km/hr\,\,;\,{{\vec r}_A} = 0\hat i + \hat j\\…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

Same subject

Match the List\(-I\) with List\(-II\)

List \(I\)	List \(II\)
\(A\) Microwaves	\(I\) Radio active decay of the nucleus
\(B\) Gamma rays	\(II\) Rapid acceleration and deceleration of electron in aerials
\(C\) Radio waves	\(III\) Inner shell electrons
\(D\) \(X\)-rays	\(IV\) Klystron valve

Choose the correct answer from the options given below

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