judy (mass 40kg) standing on slippery ice, catches her dog atti(mass 15kg) leaping toward her at 3.0 m/s. Use conservation of momentum to show that the speed of judy and her dog after the catch is 0.8 m/s .

Question

mathstudent55 · Answer

Mj = mass of Judy
Md = mass of dog
Sj = speed of Judy
Sd = speed of dog
M(j+d) = mass of Judy + dog (after Judy catches dog)
S(j+d) = speed of Judy and dog (after Judy catches dog)

MjSj + MdSd = M(j+d)S(j+d)
40 kg * 0 m/s + 15 kg * 3.0 m/s = (40 + 15)kg(S(j+d))
45 kg-m/s = 55 kg(S(j+d))
S(j+d) = 0.8 m/s

anonymous · Answer

@mathstudent55 wow is that the entire answer or is there more steps to it

anonymous · Answer

i had the first part but not the second part

mathstudent55 · Answer

That's it. Conservation of momentum means that the two bodies separately (before the catch) have as much momentum as they have together (after the catch).
Judy is at rest Sj = 0 m/s; the dog is moving at speed 3.0 m/s. The momentum of each one is the mass times the speed. Then you add their separate momentums to find the total momentum in the system.
After the catch, they act as one body with a combined weight of 40 kg + 15 kg. You solve for the speed after the catch.