Question

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 hopes 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, the kinetic energy of the smaller child compared with that of the larger child is
A. greater
B. less
C. equal

(ii) Upon reaching the water, the speed of the smaller child compared with that of the larger child is
A. greater
B. less
C. equal

(iii) During their motion from the platform to the water, the average acceleration of the smaller child compared with that of the larger child is
A. greater
B. less
C. equal

Answer 1

To answer this question, we make use of the concept of kinetic energy, mass, momentum. We imagine the accurate situation given in the question. Assume, the weight of smaller child be less than that of bigger child and frictionless slide exerts no force on the bigger child.

Complete step by step answer:
Let us imagine the given situation. Two children are standing on a platform on the top of the curving slide next to the swimming pool. Smaller child jumps directly into the pool and a bigger child slides through the curving slide. We know that, Kinetic energy of the body is given by,
$K = \dfrac{1}{2}m{v^2}$
Where, $m$ - mass of the body and $v$ - velocity of the body.

(i) The kinetic energy is proportional to mass. And the mass of a smaller child is less than that of a bigger child. Hence, Upon reaching the water, the speed of the smaller child compared with that of the larger child is less.

Hence, option B is correct.

(ii) The velocity of the smaller child is given by the velocity of the freely falling body under the action of gravity. The bigger child is sliding on the frictionless slide, hence, it also appears to be the velocity of a freely falling body under the action of gravity. Thus, Upon reaching the water, the speed of the smaller child compared with that of the larger child is equal.

Hence, option C is correct.

(iii) The acceleration of the smaller child is equal to the acceleration of gravity of the earth. But, the acceleration of the bigger child is the component of the acceleration of gravity of the earth. So, the average acceleration of the smaller child compared with that of the larger child is greater.

Hence, option A is correct.

Note: Kinetic energy of the body is directly proportional to mass and velocity of the body. The momentum of the body is related to kinetic energy of the body by Newton’s 2nd law of motion which is the rate of change of momentum of the body is directly proportional to external force applied on the body.