A bat strikes a 0.145 kgkg baseball. Just before impact, the ball is traveling horizontally to the right at 50.0 m/sm/s; when it leaves the bat, the ball is traveling to the left at an angle of 30∘30∘ above horizontal with a speed of 38.0 m/sm/s. The ball and bat are in contact for 1.75 msms. find the horizontal and vertical components of the average force on the ball.

Answer with Explanation:

We are given that

Mass of ball=m=0.145 kg

Initially horizontal  velocity of ball,ux=50 m/s

Final velocity of ball,v=38m/s

Time ,t=1.75 ms=

Horizontal component of average force,

Using the formula

Horizontal component of average force, N

Vertical component of average force,

Vertical component of average force,

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 .