A mass m moving horizontally (along the x-axis) with velocity v collides and sticks to a mass of 3m moving vertically upward (along the y -axis) with velocity 2 v. The final velocity of the combination is

Question

A mass m moving horizontally (along the x-axis) with velocity v collides and sticks to a mass of 3m moving vertically upward (along the y -axis) with velocity 2 v. The final velocity of the combination is (A) (3/4) v hat i + (1/4) v hat j (B) (1/4) v hat i + (3/2) v hat j (C) (1/3) v hat i + (2/3) v hat j (D) (2/3) v hat i + (1/3) v hat j

Tardigrade Admin · Accepted Answer

From the law of conservation of linear momentum mv hat i +(3 m )(2 v ) hat j =4 mv ' v'=(v/4) hati+(3/2) v hatj

Q. A mass $m$ moving horizontally (along the $x$ -axis) with velocity $v$ collides and sticks to a mass of $3 m$ moving vertically upward (along the $y$ -axis) with velocity $2 v$ . The final velocity of the combination is

$\frac{3}{4} v \hat{i} + \frac{1}{4} v \hat{j}$

$\frac{1}{4} v \hat{i} + \frac{3}{2} v \hat{j}$

$\frac{1}{3} v \hat{i} + \frac{2}{3} v \hat{j}$

$\frac{2}{3} v \hat{i} + \frac{1}{3} v \hat{j}$

From the law of conservation of linear momentum
$m v \hat{i} + (3 m) (2 v) \hat{j}$
$= 4 m v^{'}$
$v^{'} = \frac{v}{4} \hat{i} + \frac{3}{2} v \hat{j}$

Q. A mass m moving horizontally (along the x-axis) with velocity v collides and sticks to a mass of 3m moving vertically upward (along the y -axis) with velocity 2v. The final velocity of the combination is

43​vi^+41​vj^​

41​vi^+23​vj^​

31​vi^+32​vj^​

32​vi^+31​vj^​