Physics - Kinematics Question with Solution | TestHub

PhysicsKinematicsRelativeEasy2 minPYQ_2020

PhysicsEasynumerical

Two balls $A$ and $B$ are projected from the same position with horizontal velocity $20 m s^{- 1}$ and $5 m s^{- 1}$ as shown. The separation between these two bodies at the moment their velocities become perpendicular to each other is $x m$ . The value of $x$ is

Answer:

25.00

Solution:

$\vec{v_{1}} = 5 \hat{i} - g t \hat{j} \Rightarrow u_{1} = 5$

$\vec{v_{2}} = 20 \hat{i} - g t \hat{j} \Rightarrow u_{2} = 20$

As $\vec{v_{1}}$ and $\vec{v_{2}}$ are perpendicular,

${\vec{v}}_{1} \cdot {\vec{v}}_{2} = 0$
$t = \frac{\sqrt{u_{1} u_{2}}}{g}$
${\vec{s}}_{rel} = {\vec{u}}_{rel} \times t$
$= (u_{1} + u_{2}) t$
$= (u_{1} + u_{2}) \frac{\sqrt{u_{1} u_{2}}}{g}$
$= 25 \times \frac{10}{10} = 25 m$

Subject:PhysicsTopic:KinematicsSubtopic:Relative

⏱ 2mℹ️ Source: PYQ_2020

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