Physics Homework: Solving Vectors in a Collision

[BilloRani2012]

Homework Statement

A car weighing m kg, and a truck, weighing 4m kg, collide at an angle of alpha. Initially they are traveling at the same velocity. After the collision they move off together at an angle of theta.

a) show that tan(theta) = (4 sin alpha) / (4 cos alpha + 1)

b) Show that if their initial velocity is u the velcoity that they move off at is
v = u/5 squareroot of (17+8 cos alpha)

c) Find the velocity and direction they move off at if alpha = pi/2. What value of alpha gives the minimum velocity?

Homework Equations

The Attempt at a Solution

Ive done a) and b). BUT for part c) do i just sub alpha=pi/2 into the equation to find v. But the u is unknown too...so what do i do?

 

[CompuChip]

Yes, if you plug in alpha = pi / 2 that will give you the velocity that they move off at. The direction is given by the expression you had earlier.

For the minimum value... how do you calculate the minimum of a function? When you do the calculation, you can treat u as a constant.

 

[BilloRani2012]

okay...

i put pi/2 for alpha and got a v = square root of 17u/5. Is that right?

but how do i find the direction. You said The direction is given by the expression you had earlier. Do mean the direction is given by this expression: tan theta = 4 sin alpha / 4 cos alpha + 1 ??

 

[BilloRani2012]

i really need help for part c) becuase in the equation there is 2 unknowns --> u and alpha??
so i do i find the minimum value of alpha??

 

[BilloRani2012]

so how do i find the minimum value for alpha?