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

`v_3 = 876.17\ m/s`

Step-by-step 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* 202 = - 4.5* 422+ 8*v_3`

`v_3 = (22* 202+ 4.5* 422)/(8)`

`v_3 =792.87`

in y direction

`mv = +m_1v_1 + m_3v_3`

`0 = +9.5* 314 + 8 v_3`

`v_3 =-372.875`

now,

`v_3 = √(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`