A boy of mass $m k g$ boards a trolley of mass $2 m$ moving with a constant speed $u$ along a horizontal track. Neglecting friction, if the body jumps vertically up with reference to the trolley to catch hold of a branch of a tree, the speed of trolley after the body has jumped off is :

u

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2 u

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\frac{u}{2}

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\frac{3 u}{4}

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Solution

The correct option is A $u$
By conservation of momentum
$(m + 2 m) u = m u + 2 m V$
or $3 m u = m u + 2 m V$
or $V = u$
The vertical motion does not affect the horizontal motion. Hence the trolley moves with $u$ .

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A boy of mass m kg boards a trolley of mass 2 m moving with a constant speed u along a horizontal track. Neglecting friction, if the body jumps vertically up with reference to the trolley to catch hold of a branch of a tree, the speed of trolley after the body has jumped off is :

The correct option is A uBy conservation of momentum (m+2m)u=mu+2mVor 3mu=mu+2mVor V=uThe vertical motion does not affect the horizontal motion. Hence the trolley moves with u.

A boy of mass $m k g$ boards a trolley of mass $2 m$ moving with a constant speed $u$ along a horizontal track. Neglecting friction, if the body jumps vertically up with reference to the trolley to catch hold of a branch of a tree, the speed of trolley after the body has jumped off is :

The correct option is A $u$
By conservation of momentum
$(m + 2 m) u = m u + 2 m V$
or $3 m u = m u + 2 m V$
or $V = u$
The vertical motion does not affect the horizontal motion. Hence the trolley moves with $u$ .