A car, weighing m kg, and a truck, weighing 4m kg, collide at an angle of A .
Initially they are traveling at the same velocity. After the collision they move off together at an angle of B conserving momentum (moves off together).
a) Show that tan() =
4 sin A divided by
4 cos A + 1
.
b) Show that if their initial velocity is u the velocity that they move off at is
v =
u/5 sqrt (17 + 8 cos ).
c) Find the velocity and direction they move off at if A= pi/2

2
What value of A gives the minimum velocity?

Question

A car, weighing m kg, and a truck, weighing 4m kg, collide at an angle of A .
Initially they are traveling at the same velocity. After the collision they move off together at an angle of B  conserving momentum (moves off together).
a) Show that tan() =
4 sin A divided by
4 cos A + 1
.
b) Show that if their initial velocity is u the velocity that they move off at is
v =
u/5 sqrt (17 + 8 cos ).
c) Find the velocity and direction they move off at if  A= pi/2

2
What value of A gives the minimum velocity?

anonymous · Answer

a)from the conservation of LINEAR momentum-

$$m*\cos o +4m*\cos A =(m+4m)\cos B=5mcos B$$
$$msin 0+4msin A= 5\sin B$$
[above two are get by resolving the momentum into horizontal & perpendicular components ]

so,$$\tan B= (5\sin B)/(5\cos B)$$
$$=4msin A/(m+4mcos A)$$
$$=4\sin A /(1+4\cos A)$$