A ball of mass 2m is traveling EAST with a velocity of 2v. A ball of m is traveling NORTH with a velocity of 3v. The balls stick together (they are both made out of putty). How fast are they going immediately after they stick together? In what direction are they going immediately after they stick together?

Answer 1

momentum east = 4 v m
momentum north = 3 v m

final mass = 7 m

final v east = 4 v m/7m = (4/7) v
final v north = 3 v m/7m = (3/7) v

speed magnitude = (v/7)sqrt (16+9)

T = angle above x (east) axis
tan T = 3/4
T = 36.9 deg and thus angle clockwise from north = 53.1 on gyrocompass

Answer 2

Given:
M1 = 2m, V 1 = 2v.
M2 = m, V2 = 3v.[90o].

V3 = Velocity of M1 and M2 after collision.

Momentum before = Momentum after:
M1*V1 + M2*V2 = M1*V3 + M2*V3.
2m*2v + m*3vi = 2m*V3 + m*V3,
Divide both sides by m:
4v + 3vi = 3V3,
3V3 = 5v[36.9o],
V3 = 1.67v[36.9o].

Tan A = 3v/4v = 0.75, A = 36.9o.