Three identical balls are thrown from the top of a building, all with the same initial speed but at different angles. Neglecting air resistance, rank the speeds of the balls at the instant each hits the ground.

The speed of each ball would be same at the instant each hits the ground.

Explanation:

From the principle of conservation of energy we know that

PE₁ + KE₁ = PE₂ + PE₂

where PE = mgh

The initial and final potential energies would be same for each ball since all the balls are thrown from the same height.

Now what about KE ?

We know that each ball is thrown with the same initial speed so their initial kinetic energies would be same and in turn their final kinetic energies must be same in order to satisfy th e conservation of energy principle. Therefore, we can conclude that the speed of each ball would be same at the instant they hit the ground. The initial angle of ball doesn't have any impact on the speed of the ball.

a 2,000 calorie based diet.

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 .