A cart is moving along x direction with a velocity of 4 ms -1 . A person on the cart throws a stone with a velocity of 6 ms -1 relative to himself. In the frame of reference of the cart the stone is thrown in y - z plane making an angle of 30° with vertical z axis. At the highest point of its trajectory the stone hits an object of equal mass hung vertically from branch of a tree by means of a string of length L. The stone gets embedded in the object. The speed of combined mass immediately after the embedding with reference to an observer on the ground is B
Text Solution
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……….. (i)
= (6 sin 30) 
+ (6cos 30) 
……… (ii)
= (3 
+ 3 √ √ 3 
)
Then V stone = (ii) + (i) = 4 
+ 3 
+ 3 √ √ 3 
Velocity of stone at highest point
= 4 
+ 3 
[At highest point vertical component (i.e. z component) is zero]
or speed of stone at highest point
V = 
Using conservation of momentum
mV = 2mV combined
or V combined = 
= 2.5 ms -1
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