Question

A boy of mass 50 kg jumps to a height of 0.8 m from the ground then momentum transferred by the ground to boy is:
A).400 kg m/s
B).200 kg m/s
C).800 kg m/s
D).500 kg m/s

Answer 1

In this question, we will use the relation between kinetic energy and potential energy of an object or body to find the velocity of the object. Further, this velocity will help us to find the required momentum that is transferred by the ground to the boy. Also, we will study the basics of energy and energy conservation law.
Formula used:
$mgh = \dfrac{1}{2}m{v^2}$
$p = mv$

Complete step by step solution:
As we already know that when an object or body is at a certain height there are certain changes to its kinetic and potential energy.
The relation between the potential energy and the kinetic energy in this question can be written as:
$mgh = \dfrac{1}{2}m{v^2}$
Here, m is the mass of the object or body, g is the acceleration due to gravity, h is height and v is the velocity.
From this equation, we can get the expression for velocity v as:
$v = \sqrt {2gh}$
Substituting the given values in the above expression we get:
\eqalign{ & v = \sqrt {2 \times 10 \times 0.8} \cr & \Rightarrow v = \sqrt {16} = 4m/s \cr}
Now, to find the momentum transferred by the ground to boy , we have the relation:
$p = mv$
\eqalign{& \Rightarrow p = 50 \times 4 \cr & \therefore p = 200kgm/s \cr}

Therefore, the correct option is (B) i.e., the momentum transferred by the ground to boy is given by above result.

Additional information:
As we know that the energy is defined as the ability to do work. Energy can be found in many things and can take different forms, like-kinetic energy is the energy of motion, and potential energy is energy due to an object's position or structure. Total energy of a system is given by the sum of kinetic energy and potential energy.
We also know that, according to the law of conservation of energy, energy can neither be created nor be destroyed; rather it can only be transferred from one form to another. Here, in this question electrical energy is transferred to heat energy.
We should also know about the power. It is the amount of energy transferred or converted per unit time. In the International System or S.I Unit of power is the watt. The S.I unit of power can also be written as one joule per second. Power is a scalar quantity, which means it has only magnitude not direction.

Note:
We should remember that the laws of conservation of energy can never be violated in any case. According to the law of conservation of energy, energy can neither be created nor be destroyed; rather it can only be transferred from one form to another. Also, at maximum height the kinetic energy of an object or body becomes zero and the potential energy is maximum.