Question

A 5 kg shell kept at rest suddenly splits up into three parts. If two parts of mass 2 kg each are found flying due north and east with velocity 5 m/s each, what is the velocity of third part after explosion

Answer 1

Use

P3 = root under p1²+p2²

Answer 2

Answer: The velocity of third part after explosion is $v_{3}= 10\sqrt{2}m/s$.

Explanation:

Given that,

Mass of first part $m_{1} = 2 kg$

Mass of second part $m_{2} = 2 kg$

Initial velocity u = 0

Velocity of first and second part after explosion v = 5 m/s

Using conservation of momentum

$mu= m_{1}v_{1}+m_{2}v_{2}+m_{3}v_{3}$

On X-axis

$m_{1}v_{1}+m_{3}v_{3}\ cos \theta = 0$

$2\times 5+1\times v_{3}\ cos\theta = 0$

$v_{3}\ cos\theta = -10$....(I)

On Y-axis

$m_{2}v_{2}+m_{3}v_{3}\ sin\theta = 0$

$2\times 5+v_{3}\ sin\theta = 0$

$v_{3}\ sin\theta = -10$.....(II)

On Squaring and add both of the equations

$v_{3}^2= 200 m/s$

$v_{3}= 10\sqrt{2}m/s$

Hence, The velocity of third part after explosion is $v_{3}= 10\sqrt{2}m/s$.