Answer:
<em>(a) Car A was going faster</em>
<em>(b) Car A was at 120 Km/h</em>
Explanation:
<u>Linear Momentum</u>
The momentum of an object of mass m traveling at a velocity is given by
Both the moment and the velocity are vectors. If a system of particles A and B collide and no external forces act on them, the total momentum is conserved. i.e.
Where ma, mb are the masses of the particles A and B respectively and va, vb, va' and vb' are their respective velocities before and after the collision.
The question states that after the collision, both cars get stuck which means their final velocity is common to them, and our equation becomes
(a)
We have called to the final common velocity. The car B was traveling south which means its rectangular components of the speed are
The car A was traveling 30° north of east. Its components are
After the collision, both cars travel at a velocity
Let's replace all the velocities into the above formula
Equating the x-components:
Solving for va
Equating the y-components:
Solving for vb
We can see car A was going faster than car B
(b)
If the slower car was at speed limit (50 Km/h), we will find the speed of the car A. Dividing va/vb, we get
Or equivalently