Question

A 22.0-kg body is moving in the direction of the positive x axis with a speed of 202 m/s when, owing to an internal explosion, it breaks into three pieces. One part, whose mass is 9.5 kg, moves away from the point of explosion with a speed of 314 m/s along the positive y axis. A second fragment, whose mass is 4.5 kg, moves away from the point of explosion with a speed of 422 m/s along the negative x axis. What is the speed of the third fragment? Ignore effects due to gravity.

Answer 1

Answer:

$v_3 = 876.17\ m/s$

Explanation:

given,

mass of body = 22 kg

velocity in positive x-axis direction = 202 m/s

mass of one part = 9.5 kg

velocity in y-axis = 314 m/s

mass of second fragment = 4.5 kg

speed of second fragment in negative x - axis = 422 m/s

speed of the third = ?

mass of third fragment

     m_3 = 22-9.5-4.5

     m_3 = 8 kg

in x- direction

$mv = -m_2v_2 + m_3v_3$

$22\times 202 = - 4.5\times 422+ 8\timesv_3$

$v_3 = \dfrac{22\times 202+ 4.5\times 422}{8}$

$v_3 =792.87$

in y direction

$mv = +m_1v_1 + m_3v_3$

$0 = +9.5\times 314 + 8 v_3$

$v_3 =-372.875$

now,

$v_3 = \sqrt{792.87^2+(-372.875)}$

$v_3 = 876.17\ m/s$

speed of the third fragment is equal to $v_3 = 876.17\ m/s$