Abullet of mass m is fired at speed v0 into a wooden block of mass m. the bullet instantaneously comes to rest in the block. the block with the embedded bullet slides along a horizontal surface with a coefficient of kinetic friction μ. write an expression for how far the block slides (s) in terms of m, m, vo , μ, and g.

Explanation:

mass of bullet = m

mass of block = M

initial speed of bullet = vo

coefficient of friction = μ

Let the horizontal distance traveled before stopping is s.

Let v be the velocity of the bullet and block system after collision.

Use conservation of momentum

m x vo = (M+m) x v

Now use third equation of motion

v² = u² - 2 a s

So,

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 .