Two astronauts on opposite ends of a spaceship are comparing lunches. One has an

Question

Two astronauts on opposite ends of a spaceship are comparing lunches. One has an apple, the other has an orange. They decide to trade. Astronaut 1 tosses the 0.125 kg apple toward astronaut 2 with a speed of v_i, 1 = 1.10 m/s. The 0.170 kg orange is tossed from astronaut 2 to astronaut 1 with a speed of 1.22 m/s. Unfortunately, the fruits collide, sending the orange off with a speed of 0.954 m/s in the negative y direction. What are the final speed and direction of the apple in this case? V_1, f = m/s Theta = degree counterclockwise from the positive x axis

Explanation / Answer

Mass of Apple (m1) = 0.125 k

Initial velocity (u1) = ( 1.10 i ) m/s

Mass of Orange (m2) = 0.170 kg

Initial velocity (u2) = ( - 1.22 i ) m/s

Final velocity of Orange (v2) = ( - 0.954 j ) m /s

From conservation of momentum :

     m1 u1 + m2 u2 = m1 v1 + m2 v2

   m1 v1 = (  m1 u1 + m2 u2 ) - m2 v2

      = ( 0.125 * 1.10 i + 0.170 * -1.22 i ) - ( 0.170 * -0.954 j )

      = 0.069 i + 0.1621 j

.v1 = (0.069 i + 0.1621 j) /0.125

   = 0.559 i + 1.2968 j

Hence magnitude is :

v1 = sqrt [ (0.559)2   + (1.2968)2 ]

= 1.41 m/s

Direction is :   ? = tan-1  ( 1.2968 / 0.559 ) = 89.90

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