A firecracker breaks up into two pieces, one has a mass of 200 g and files off along the x - axis with a speed of 82.0 m/s and the second has a mass of 300 g and flies off along the y-axis with a speed of 45.0 m/s. What is the total momentum of the two pieces?

a) 361 kg x m/s at 56.3 degrees from the x-axis.

b) 93.5 kg x m/s at 28.8 degrees from the x-axis.

c) 21.2 kg x m/s at 39.5 degrees from the x-axis.

d) 361 kg d m/s at 0.983 degrees from the x-axis.

A) 21.2 kg. m/s at 39.5 degrees from the x-axis

Explanation:

Mass of the smaller piece = 200g = 200/1000 = 0.2 kg

Mass of the bigger piece = 300g = 300/1000 = 0.3 kg

Velocity of the small piece = 82 m/s

Velocity of the bigger piece = 45 m/s

Final momentum of smaller piece = 0.2 * 82 = 16.4 kg. m/s

Final momentum of bigger piece = 0.3 * 45 = 13.5 kg. m/s

since they acted at 90oc to each other (x and y axis) and also momentum is vector quantity; then we can use Pythagoras theorems

Resultant momentum² = 16.4² + 13.5² = 451.21

Resultant momentum = √451.21 = 21.2 kg. m/s at angle 39.5 degrees to the x-axis (tan^-1 (13.5 / 16.4)