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  🧭 Relative Motion of Ships – Minimum Distance Concept | JEE Physics | Doubtify JEE 📌 Question: Ship A is sailing towards north-east with velocity v = 30 î + 50 ĵ km/h , where î points east and ĵ points north . Ship B is at a distance of 80 km east and 150 km north of Ship A and is sailing west at 10 km/h . 🔍 Find the time at which Ship A is at minimum distance from Ship B. 🖼️ Question Image:

    🧲 Motion in a Plane  |  Physics |  Doubtify JEE 💡 Question: A mosquito is moving with a velocity  v = 0.5 t² î + 3t ĵ + 9 k̂ m/s and accelerating in uniform conditions. What will be the direction of motion of the mosquito after 2 seconds? 🖼️ Question Image: 🔬 Concept Overview: This is a vector motion problem where you're given a time-dependent velocity vector in three dimensions. To find the direction of motion , we must compute the velocity vector at  t = 2 t  =  2 seconds and then determine its direction using unit vector analysis or angle calculation with respect to axes. This is a key concept from the chapter "Motion in a Plane" , often asked in JEE Mains or Advanced. 🧠 Step-by-Step Explanation: Given: v ⃗ ( t ) = 0.5 t 2 i ^ + 3 t j ^ + 9 k ^ \vec{v}(t) = 0.5t^2 \hat{i} + 3t \hat{j} + 9 \hat{k} At t = 2 t = 2  seconds: i-component: 0.5 × 2 2 = 2   m/s j-component: 3 × 2 = 6   m/s 3 \times 2 = 6 \, \text{m/s} ...