Acar of mass 2800 kg collides with a truck of mass 4000 kg, and just after the collision the car and truck slide along, stuck together, with no rotation. the car's velocity just before the collision was < 36, 0, 0> m/s, and the truck's velocity just before the collision was < -15, 0, 29> m/s. (a) your first task is to determine the velocity of the stuck-together car and truck just after the collision. (d) what is the increase in internal energy of the car and truck (thermal energy and deformation)?

Final Velocity of the system = 18.07 m/s

Increase in the internal energy = 2836215.34 Joules

Explanation:

Treating the car and truck as a system we shall use the conservation of momentum to find the final velocities

Along the x axis the moumentum of each body is as under

Thus initial moumentum of the system along x direction is

Now after collision since both the car and truck move as a single unit we have

Equating the initial momentum with final momentum we get

Similarly we shall conserve the moumentum along the z direction also

Equating initial and final momentum we have

Thus the resultant velocity of the system after the collision is given by

To find the increase in the internal energy we shall use the conservation of energy principle

Initial Energy =

Similarly final energy of the system is

Thus the increase in the internal energy is the diffrence between initial and final energies

this could be newton#'s law of cooling. the cooling curve is exponential

we have been given a quadratic function and we need to restrict the domain such that it becomes a one to one function.

we know that vertex of this quadratic function occurs at (5,2).

further, we know that range of this function is .

if we restrict the domain of this function to either or , it will become one to one function.

let us know find its inverse.

upon interchanging x and y, we get:

let us now solve this function for y.

hence, the inverse function would be if we restrict the domain of original function to and the inverse function would be if we restrict the domain to .