Question

A gadget of mass 14.61 kg floats in space without motion. Because of some internal malfunction, the gadget violently breaks up into 3 fragments flying away from each other. The first fragment has mass m1 = 5.38 kg and speed v1 = 6.47 m/s while the second fragment has mass m2 = 3.92 kg and speed v2 = 7.73 m/s. The angle between the velocity vectors ⃗v1 and ⃗v2 is θ12 = 43◦.

What is the speed v3 of the third fragment? Answer in units of m/s.

Answer 1

mass of third part is m3 = m-(m1+m2) = 14.61-5.38-3.92 =5.31 kg

assume that m1 is along X-axis

m2 makes an angle is 43 degrees with x-axis

and m3 makes an angle theta with x-axis

Using law of conservation of momentum

along X-axis

0 = (5.38*6.47)+(3.92*7.73*cos(43)) + (5.31*V3*cos(theta))

(5.31*V3*cos(theta)) = -56.96

v3*cos(theta) = -10.72 m/sec.........(1)

along y-axis

0 = 0 + (3.92*7.73*sin(43)) + (5.31*V3*sin(theta))

(5.31*V3*sin(theta)) = - 20.66 m/sec

v3*sin(theta) = -3.89 m/sec...........(2)

(2)/(1) tan(theta) = 3.89/10.72

theta = tan^(-1)(3.89/10.72) = 20 degrees

v3*sin(20) = -3.89

v3 = -3.89/sin(20) =-11.4 m/sec

speed v3 = 11.4 m/sec