After several large firecrackers have been inserted into it\'s holes (giggity),

Question

After several large firecrackers have been inserted into it's holes (giggity), a bowling ball is projected into the air using a homemade launcher and explodes in midair. During the launch, the 7-kg ball is shot into the air with an initial speed of 10 m/s at a 40o angle; it explodes at the peak of it's trajectory, breaking into three pieces of equal mass. Once piece travels straight up with a speed of 3.0 m/s. Another piece travels straight back with a spee of 2.0 m/s. What is the speed and direction of the third piece?

Please include all formulas used, show all work, and ALWAYS INCLUDE UNITS. This has been a big problem. Thanks so much!

Explanation / Answer

At peak trajectory point velocity is horizontal
vin = 10 cos(40o)

conservation of momentum

mivi = mfvf

mi = 7 kg (intial mass of the ball)

vinitial = 7.66 i m/sec

mf --> 3 pieces of equal mass= mi /3

mf / mi = 3

velocities of

1st piece = 3.0j m/s as travels straight up

2nd piece = travels straight back with a spee of 2.0 = -2i

from equation 3rd piece = 3*7.66 i - 3.0j + 2i = 24.98i - 3j

velocity magnitude is 25.16 m/sec and direction is Tan-1(-3/24.98) = -6.85o

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