Question

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

• A. 2.5 ms^-1
• B. 1.5 ms^-1
• C. 5.2ms^-1
• D. 3.5ms^-1.

Answer 1

Answer: (A)

2.5 ms^-1

Answer 2

${\overrightarrow{V}}_{cart} = 4\widehat{i}$ ……….. (i)

${\overrightarrow{V}}_{stone + cart}$ = (6 sin 30)$\widehat{j}$ + (6cos 30)$\widehat{k}$ ……… (ii)

= (3$\widehat{j}$ + 3√3$\widehat{k}$)

Then V_stone = (ii) + (i) = 4$\widehat{i}$ + 3$\widehat{j}$ + 3√3$\widehat{k}$

Velocity of stone at highest point

${\overrightarrow{V}}_{stone + height}$ = 4$\widehat{i}$ + 3$\widehat{j}$

[At highest point vertical component (i.e. z component) is zero]

or speed of stone at highest point

V = $\sqrt{4^{2} + 3^{2}} = \sqrt{16 + 9} = 5ms^{- 1}$Using conservation of momentum

mV = 2mV_combined

or V_combined = $\frac{V}{2} = \frac{5}{2}$= 2.5 ms^-1