Physics - Kinematics Question with Solution | TestHub

PhysicsKinematicsRelativeMedium2 minQB

PhysicsMediuminteger

Passage / Comprehension

Ram and Shyam are walking on two perpendicular tracks with speed $3 m s^{- 1}$ and $4 m s^{- 1}$ respectively. At a certain moment (say t = 0 sec) Ram and Shyam are at 20 m and 40 m away from the intersection of tracks respectively and moving towards the intersection of the tracks.

Shortest distance between them subsequently, is ______ m.

Answer:

Solution:

Ram starts at (20, 0) moving at 3 m/s and Shyam at (0, 40) moving at 4 m/s, both toward the intersection.

Separation: $D^{2} (t) = (20 - 3 t)^{2} + (40 - 4 t)^{2}$ . Minimum when $\frac{d D ^{2}}{d t} = - 6 (20 - 3 t) - 8 (40 - 4 t) = 0$ , i.e. $50 t = 440, t = 8.8 s$ .

$D^{2} = (6.4)^{2} + (4.8)^{2} = 64 \Rightarrow D = 8 m$ . Answer: 8.

Stream:JEESubject:PhysicsTopic:KinematicsSubtopic:Relative

⏱ 2mℹ️ Source: QB

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