You and your friends are out camping and get your hands on s

You and your friends are out camping and get your hands on some fireworks. You put a firework inside a tennis ball and light the fuse. After the explosion, the ball breaks into three pieces. Two pieces with equal mass fly off north and east, respectively, both at speed v0. The third piece has twice the mass as the other two.

a. What is the speed of the third piece?

b. What direction does the third piece travel in? Give your answer as an angle from north.

Solution

a)

Conserving momentum before and after bursting:

0 = m*(vo i) + m*(vo j) + 2m*v <------- v = velocity of the third particle

i = unit vector along East direction

j = unit vector along North direction

So, v = -(vo/2)*(i+j)

So, speed of the third piece:

| v | = (vo/2)*sqrt(2) = vo/sqrt(2) <--------answer

b)

direction = atan(1/1) = 90 +45 = 135 with respect to North towards West