Question
An athlete in the Olympic games covers a distance of $$100\,m$$ in $$10 \,s.$$ His kinetic energy can be estimated to be in the range-
A.
$$200\,J-500\,J$$
B.
$$2 \times {10^5}\,J - 3 \times {10^5}\,J$$
C.
$$20,000\,J-50,000\,J$$
D.
$$2,000\,J-5,000\,J$$
Answer :
$$2,000\,J-5,000\,J$$
Solution :
The average speed of the athlete
$$v = \frac{{100}}{{10}} = 10\,m/s\,\,\,\,\,\,\,\,\,\therefore K.E. = \frac{1}{2}m{v^2}$$
If mass is 40 kg then, K.E. $$ = \frac{1}{2} \times 40 \times {\left( {10} \right)^2} = 2000\,J$$
If mass is 100 kg then, K.E. $$ = \frac{1}{2} \times 100 \times {\left( {10} \right)^2} = 5000\,J$$