During a fireworks display, a 0.270-kg bottle rocket approaches the top of its t

Question

During a fireworks display, a 0.270-kg bottle rocket approaches the top of its trajectory and explodes into two pieces as in the figure. The first piece (Piece 1) has mass 0.170 kgand the second piece (Piece 2) has mass 0.100 kg.Immediately after the explosion, the first piece is observed traveling to the left at a speed of 4.20 m/s and the second piece is observed traveling at an angle = 34.0° above the horizon at a speed of 15.0 m/s.

Determine the components of the bottle rocket's velocity immediately before the explosion.

Explanation / Answer

M = 0.27 kg , m1 =0.17 kg, m2 =0.1 kg

v1x = - 4.2 i, v1y =0

v2x = 15cos(34) i =12.44i

v2y =15sin(34) j = 8.39 j

From conservation of momentum along X-direction

Mvxi =m1v1x+m2v2x

(0.27)vxi = [-(0.17)(4.2)i]+[(0.1)(12.44)i]

vxi = 1.963i m/s

From conservation of momentum along Y-direction

Mvyi =m1v1y+m2v2y

(0.27)vyi = 0+[(0.1)(8.39)i]

vyi =3.11j m/s

vxi = 1.963 m/s

vyi = 3.11 m/s

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