A 2.0kg ball is resting at the top of a 20 m hill. if the ball rolls down the entire hill, how fast will it be going?

Speed of ball is 19.80 m/s .

Explanation:

We have , a 2.0 kg ball is resting at the top of a 20 m hill. if the ball rolls down the entire hill,We need to find how fast will it be going.Let's find out:

We know that,

Potential energy : This is the energy possessed by an object due to it's virtue of height and is given by , where m is mass , g is acceleration due to gravity & h is height !

Kinetic energy : This is the energy possessed by an object due to it's virtue of motion and is given by , where m is mass & v is the velocity of object !

By conservation of energy :

⇒

⇒

⇒

According to question , h=20 m i.e.

⇒

⇒

⇒

Hence , Speed of ball is 19.80 m/s .

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 .

answer: 31, 5556. 952 seconds