Question

A girl weighing $50Kg$ makes a high jump of $1.2m$. What is her kinetic energy at the highest point? $\left( g=10m/{{s}^{2}} \right)$
$A)\text{ }6000J$
$B)\text{ }600J$
$C)\text{ }60J$
D) Zero

Answer 1

Hint: This problem can be solved by realizing the fact that the kinetic energy of a body depends upon the speed of the body. Also, when the girl jumps, at the highest point she momentarily comes to rest, that is, her speed becomes zero.

Formula used: $KE=\dfrac{1}{2}m{{v}^{2}}$

Complete step by step answer:
The kinetic energy of a body is the energy possessed by a body by virtue of its motion.
The kinetic energy $KE$ of a body of mass $m$ and moving at speed $v$ is given by
$KE=\dfrac{1}{2}m{{v}^{2}}$ --(1)
Now, let us analyze the question.
We have to find out the kinetic energy of the girl at the highest point of her jump.
Let this be $KE$.
Now, at the highest point of her jump, she momentarily comes to rest before starting to come down again. This is in fact true for all bodies that are thrown upwards or move upwards and then fall back down due to the effect of gravity.
Therefore, the speed of the girl at the highest point will be $v=0$.
Hence, using (1), we get the kinetic energy as
$KE=\dfrac{1}{2}m{{\left( 0 \right)}^{2}}=0$
where $m$ is the mass of the girl.
Therefore, the kinetic energy of the girl at the highest point of her jump will be $0$.

So, the correct answer is “Option D”.

Note: Students must note that the potential energy of the girl at the highest point of the jump will be maximum and equal to the kinetic energy of the girl when she just started to jump. This is because the sum of the potential energy and the kinetic energy (which is the mechanical energy) of a body remains constant when acted upon by a conservative force such as gravity. Hence, at the highest point of the jump, the potential energy will be maximum and kinetic energy will be minimum while at the lowest point, the kinetic energy will be maximum and the potential energy minimum.