A man of mass m is standing on the flat top of a cart of mass 2m. The length and height of the cart is L and H respectively and it is at rest on a smooth horizontal ground. The man starts running from

Question

A man of mass m is standing on the flat top of a cart of mass 2m. The length and height of the cart is L and H respectively and it is at rest on a smooth horizontal ground. The man starts running from end A, speeds up and jumps out of the cart at point B with a velocity 'u' relative to the cart in horizontal direction. The total horizontal distance covered by the man by time he lands on the ground.

TestHub · Accepted Answer

While the man runs A→B, COM stays fixed: man covers 3 2 L ​ over ground (cart shifts 3 L ​ back). Jump: momentum conservation m ( u + V c ​ ) + 2 m V c ​ = 0 ⇒ V c ​ = − 3 u ​ , so man's ground speed = 3 2 u ​ . Flight time g 2 H ​ ​ adds 3 2 u ​ g 2 H ​ ​ . Total = 3 2 L ​ + 3 2 u ​ g 2 H ​ ​ . Answer: (D)

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