A stationary shell explodes into 3 pieces

Question

A stationary shell explodes into 3 pieces. 3kg piece travels north. two other fragments travel opposite directions of south west 25 degrees and south east 25 degrees. What is the speed of each of the 2 kg fragments if the speed of the 3 kg fragment is 10 m/s

 

Im getting an answer of 8.3m/s but i think it might be wrong. the answer choices are:

a. 7.5 m/s

b. 3.8 m/s

c. 8.3 m/s

d. 5.0 m/s

e 4.2 m/s

Answer 1

I assume the given angles are from the north-south line (which is not stated clearly in the problem).  Linear momentum must be conserved, so each component of linear momentum after the explosion must be zero.  The north momentum must be equal and opposite to the south momentum.

 

p_N = p_S

 

(3 kg)(10 m/s) = 2(2 kg)v cos25°

 

v = (30 / 4cos25°) m/s ≅ 8.3 m/s

 

Your answer is correct, based on this interpretation of the angles.