Mass of the mine car = m1 = 440 kg
Mass of the chunk of coal = m2 = 150 kg
Initial velocity of the mine car = V1 = 0.5 m/s
Initial velocity of the chunk of coal = V2 = 0.8 m/s
Angle of velocity of the chunk of coal = = 25o
Initial velocity of the chunk of coal in the horizontal direction = V2x = V2Cos = (0.8)Cos(25) = 0.725 m/s
Final velocity of the car-coal system = V3
The final velocity will be in the horizontal direction.
Conserving the momentum in the horizontal direction.
m1V1 + m2V2x = (m1 + m2)V3
(440)(0.5) + (150)(0.725) = (440 + 150)V3
V3 = 0.557 m/s
Speed of the car-coal system after the coal has come to rest in the car = 0.557 m/s
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