A body of mass 1 , kg is projected from the g | vedclass

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(A) The initial velocity of the body is $\vec{u} = u \cos 	heta \hat{i} + u \sin 	heta \hat{j}$.At the end of the flight (when it returns to the gro

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$50$

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(A) The initial velocity of the body is $\vec{u} = u \cos 	heta \hat{i} + u \sin 	heta \hat{j}$.At the end of the flight (when it returns to the ground),the velocity is $\vec{v} = u \cos 	heta \hat{i} - u \sin 	heta \hat{j}$.The change in momentum is $\Delta \vec{p} = m\vec{v} - m\vec{u} = m(\vec{v} - \vec{u})$.$\Delta \vec{p} = m(u \cos 	heta \hat{i} - u \sin 	heta \hat{j} - (u \cos 	heta \hat{i} + u \sin 	heta \hat{j}))$.$\Delta \vec{p} = m(-2u \sin 	heta \hat{j})$.The magnitude of the change in momentum is $|\Delta \vec{p}| = 2mu \sin 	heta$.Given $m = 1 \, kg$,$u = 50 \, m/s$,and $	heta = 30^{\circ}$.$|\Delta \vec{p}| = 2 	imes 1 	imes 50 	imes \sin 30^{\circ} = 100 	imes 0.5 = 50 \, kg \cdot m/s$.

Column $I$	Column $II$
$(A)$ Horizontal component of velocity	$(p)$ $5$ $SI$ unit
$(B)$ Vertical component of velocity	$(q)$ $10$ $SI$ unit
$(C)$ Horizontal displacement	$(r)$ $15$ $SI$ unit
$(D)$ Vertical displacement	$(s)$ $20$ $SI$ unit

$A$ body of mass $1 \, kg$ is projected from the ground at an angle of $30^{\circ}$ with the horizontal on level ground at a speed of $50 \, m/s$. The magnitude of the change in momentum of the body during its entire flight is ....... $kg \cdot m/s$ $(g = 10 \, m/s^2)$.

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