With the batsman at the origin, a fielder stands at ( 24 i ^ + 32 j ^ ) m and the ball rolls with constant velocity ( 6 i ^ + 8 j ^ ) m / s . The fielder runs at 5 m / s starting immediately. The shortest interception time is:

( 6 t − 24 ) 2 + ( 8 t − 32 ) 2 = 25 t 2 gives 3 t 2 − 32 t + 64 = 0 , t = 6 32 ± 16 ; shortest t = 6 16 = 3 8 s .

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Physics - Kinematics Question with Solution | TestHub

PhysicsKinematicsRelativeMedium3 minQB

PhysicsMediumnumerical

With the batsman at the origin, a fielder stands at $(24 \hat{i} + 32 \hat{j}) m$ and the ball rolls with constant velocity $(6 \hat{i} + 8 \hat{j}) m / s$ . The fielder runs at $5 m / s$ starting immediately. The shortest interception time is:

Answer:

2.67

Solution:

$(6 t - 24)^{2} + (8 t - 32)^{2} = 25 t^{2}$
gives
$3 t^{2} - 32 t + 64 = 0, t = \frac{32 \pm 16}{6}$ ;
shortest
$t = \frac{16}{6} = \frac{8}{3} s$ .

Stream:JEESubject:PhysicsTopic:KinematicsSubtopic:Relative

⏱ 3mℹ️ Source: QB

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