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(A) Let the velocity of the wedge be $v$ and the velocity of the ball relative to the wedge be $u$ along the incline.By conservation of momentum in th

Vedclass · Accepted Answer

$\frac{2v^2}{g}$

Vedclass · Answer

(A) Let the velocity of the wedge be $v$ and the velocity of the ball relative to the wedge be $u$ along the incline.By conservation of momentum in the horizontal direction: $m v - m(u \cos 45^{\circ} - v) = 0$,which simplifies to $v = u \cos 45^{\circ} - v$,so $u \cos 45^{\circ} = 2v$.Thus,the horizontal component of the ball's velocity relative to the ground is $v_x = u \cos 45^{\circ} - v = 2v - v = v$.The vertical component of the ball's velocity relative to the ground is $v_y = u \sin 45^{\circ} = 2v$ (since $\sin 45^{\circ} = \cos 45^{\circ}$).After an elastic collision with the floor,the vertical component of the velocity is reversed,but the magnitude remains $v_y = 2v$.The maximum height $H$ attained by the ball is given by $H = \frac{v_y^2}{2g} = \frac{(2v)^2}{2g} = \frac{4v^2}{2g} = \frac{2v^2}{g}$.

Column-$I$	Column-$II$
$(1)$ Definition of force	$(a)$ Newton's third law of motion
$(2)$ Measurement of force	$(b)$ Newton's second law of motion
	$(c)$ Newton's first law of motion

$A$ ball of mass $m$ is released from the top of a smooth movable wedge of mass $m$. When the ball collides with the floor,the velocity of the wedge is $v$. Then the maximum height attained by the ball after an elastic collision with the floor is: (Neglect any edge at the lower end of the wedge).

Similar Questions

$A$ bird is sitting in a large closed cage which is placed on a spring balance. It records a weight of $25 \, N$. The bird (mass $m = 0.5 \, kg$) flies upward in the cage with an acceleration of $2 \, m/s^2$. The spring balance will now record a weight of ........ $N$.

Match the items in Column-$I$ with those in Column-$II$.

Column-$I$ Column-$II$

$(1)$ Definition of force $(a)$ Newton's third law of motion

$(2)$ Measurement of force $(b)$ Newton's second law of motion

$(c)$ Newton's first law of motion

Three forces $\vec{F}_1=(2 \hat{i}+4 \hat{j}) \,N$,$\vec{F}_2=(2 \hat{j}-\hat{k}) \,N$,and $\vec{F}_3=(\hat{k}-4 \hat{i}-2 \hat{j}) \,N$ are applied on an object of mass $1 \,kg$ at rest at the origin. The position of the object at $t=2 \,s$ will be:

$A$ $10 \,g$ bullet moving at $200 \,m/s$ stops after penetrating $5 \,cm$ of a wooden plank. The average force exerted on the bullet will be .......... $N$.

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