Question

Two cars collide at an intersection. Car A, with a mass of 1800 kg , is going from west to east, while car B , of mass 1300 kg , is going from north to south at 16 m/s . As a result of this collision, the two cars become enmeshed and move as one afterwards. In your role as an expert witness, you inspect the scene and determine that, after the collision, the enmeshed cars moved at an angle of 55^∘ south of east from the point of impact.

A : How fast were the enmeshed cars moving just after the collision? Express your answer using two significant figures.

B: How fast was car A going just before the collision? Express your answer using two significant figures.

Answer 1

For Car A:
p=mv
p=1800*u Ns (use u as velocity so there is no confusion later on)
For Car B:
p=mv
p=1300*16
p=20800 Ns
For Enmeshed Cars:
m=1300+1800
m=3500kg
p=mv
p=3100*v Ns
Resolve Vectors:
theta=55 degrees
Adjacent=1800*u
Opposite = 20800
Hypotenuse=3100*v

A)
sin(theta)=O/H
sin(65)= 20800/(3100*v)
v=20800/(3100*sin(55))
v=8.19m/s
The enmeshed cars are moving at 8.19m/s.

B)
tan(theta)=O/A
tan(55)=20800/(1800*u)
u=20800/(1800*tan(55))
u=8.09m/s
Car A is moving at 8.09m/s, just before the collision.