Mechanics question

Question

A mass 3m moving east at a speed v collides with a mass 2m moving northeast at a speed 2v. The masses stick together what is the resulting speed and direction of the combined mass. 

Answer 1

Linear momentum must be conserved in both the east and north directions.

 

East:

 

(3m)v + (2m)(2v)cos45° = (3m + 2m)v_E = 5mv_E ⇒

 

v_E = (1/5)(3 + 4cos45°)v

 

North:

 

(3m)(0) + (2m)(2v)sin45° = 5mv_N ⇒

 

v_N = (4/5)(sin45°) v

 

Resulting speed:

 

v_r = √(v_E² + v_N²) = ?

 

Plug in v_E and v_N, evaluate, and simplify.

 

Direction north of east:

 

θ = arctan(v_N/v_E)

 

Plug in v_E and v_N, evaluate, and simplify.  You can finish from here.