Two children stand on a platform at the top of a curving slide next to a backyard swimming pool. At the same moment the smaller child hops off to jump straight down into the pool, the bigger child releases herself at the top of the frictionless slide.

(i) Upon reaching the water, how does the kinetic energy of the smaller child compare with that of the larger child?

a. It is greater. b. It is less. c. The two energies are equal.

(ii) Upon reaching the water, how does the speed of the smaller child compare with that of the larger child is?

a. It is greater. b. It is less. c. The two speeds are equal.

(iii) During their motions from the platform to the water, how does the average acceleration of the smaller child compare with that of the larger child? a. It is greater. b. It is less. c. The two accelerations are equal.
d. The First and third are wrong

Explanation:

i )

In a conservative field like gravitational field , loss of potential energy  or work done , depends upon the initial and final point and not the manner in which 2 nd point has been reached . Since the initial and final point is same in both the cases of straight and curved path , final velocity will remain same for both of them .

Hence , due to increased mass of larger child , his kinetic energy will be greater .

ii ) Since the initial and final point is same in both the cases of straight and curved path , final velocity will remain same for both of them .

iii ) Smaller child undergo free fall , therefore , he will fall with acceleration g . The larger child falls on curved path . So , he will have only a component of

vertical g at any moment  . hence average acceleration  will be less.

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 .