A space probe, initially at rest, undergoes an internalmechanical malfunction an

Question

A space probe, initially at rest, undergoes an internalmechanical malfunction and breaks into three pieces. One piece ofmass m1 = 41.3 kgtravels in the position x-direction at 12.0 m/s, and asecond piece of mass m2 = 62.0 kg travels inthe xy-plane at an angle of 105° at 15.6 m/s. The third piece has massm3 = 112 kg. c) Solve the two-momentum equations for v3cos and v3 sin ,respectively, and use the identity cos2+ sin2 = 1 to obtainv3 (m/s) d)Divide the equation for v3 sin by v3 cos toobtain tan , then obtain the angle by taking theinverse tangent of both sides. (m/s)

Explanation / Answer

a) x component of m1 = mass* velocity in x direction = 41.3*12.0 =495.6 kgm/s x component of m2 = mass* velocity in x direction = 62.0*15.6*cos(105o) = -242.25 kgm/s b)y component of m1 = mass* velocity in y direction = 41.3*0= 0 kgm/s y component of m2 = mass* velocity in y direction = 62.0*15.6*sin(105o) = 934.24 kgm/s But initial momentum of ship was zero . so total final momentumwill also be zero . so 112*v3 cos +495.6-242.25 = 0 v3 cos = -2.26 Similarly , v3 sin +0+934.24 = 0 => v3 sin = -8.34 using the identity cos2 +sin2 = 1 to obtainv3 v3 = 8.64 m/s =tan-1(-8.34/-2.26) = 180 +74.84 =254.84o(velocity will be towards third quadrant )

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