Consider east-west direction along the x-axis with east pointing towards positive x-axis.

Consider north-south direction along the y-axis with north pointing towards positive y-axis.

V = initial velocity of three pieces of coconut together before blast = 0 m/s

m₁ = mass of the piece moving towards south = m

v₁ = velocity of the piece moving towards south = 0 i - v₀ j

m₂ = mass of the piece moving towards west = m

v₂ = velocity of the piece moving towards west = - v₀ i + 0 j

m₃ = mass of the third piece = 2 m

v₃ = velocity of the third piece

using conservation of momentum

(m₁ + m₂ + m₃ ) V = m₁ v₁ + m₂ v₂ + m₃ v₃

inserting the values

(m + m + 2 m ) (0) = m (0 i - v₀ j) + m (- v₀ i + 0 j) + (2m) v₃

0 = m (0 i - v₀ j) + m (- v₀ i + 0 j) + (2m) v₃

0 = - (mv₀) j - (m v₀) i + (2m) v₃

0 = - (v₀) j - (v₀) i + (2) v₃

v₃ = (0.5) v₀ i + (0.5) v₀ j

speed : Sqrt(((0.5) v₀)² + ((0.5) v₀)²) = (0.71) v₀

θ =angle east of north = tan⁻¹((0.5) v₀)/(0.5) v₀)) = tan⁻¹(1) = 45 degree