Question

One yak, (m1) with a mass 500 kg is sitting still on a frictionless surface when a smaller yak (m2) charges into it at a velocity of 15 m/s in a direction 30° north of west. After the two collide the smaller yak is traveling due west while the larger yak is traveling due north. The smaller yak’s final speed is twice that of the larger yak.

(a) What is the mass of the smaller yak?

(b) What is the final speed of the smaller yak?

(c) Use Proportionality in conjunction with Special Cases sense-making to check your answer in part (b). How would the final speed change as their masses get more disparate or closer together? What happens as the ratio of the masses goes to zero or infinity?

Answer 1

[Before mu CAfter) In or direction m, vi & mg Voi - m, ug & mast 5000ot. may 15x as 30°- o- may, i t In y- direction, -- max 15x sin 3° = m, x vif -max7.5 = 500 x

We have two equations, - 13 m₂ = -movog -7.5 m₂ =500 vig OR - = 3 mgz m. /vag = -13 m/s) To the west -7.5 mg = 500 X vt -7.5 mg - 5008 E 13 mg = 433.33 kg As masses increase come close the velocities for both m, and ma.