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Kinetic Energy

The picture a...

Question

The picture above shows five identical bugs flying with five different speeds at five different heights as shown. How does the kinetic energy of bug # 1, $K_{1}$ compare to the kinetic energy of bug # 5, $K_{5}$ and how does the gravitational potential; energy of bug # 1, $U_{1}$ compare to that of bug # 5, $U_{5}$ ?

K_{1} > K_{5}, U_{1} > U_{5}

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K_{1} < K_{5}, U_{1} < U_{5}

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K_{1} < K_{5}, U_{1} > U_{5}

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K_{1} > K_{5}, U_{1} < U_{5}

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K_{1} = K_{5}, U_{1} = U_{5}

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Solution

The correct option is C $K_{1} < K_{5}, U_{1} > U_{5}$

Kinetic energy is given by
$K . E . = \frac{1}{2} m v^{2}$
Potential Energy is given by
$P . E . = m g h$
Thus,
$K_{1} = \frac{1}{2} m {(1)}^{2} = \frac{m}{2} K_{5} = \frac{1}{2} m {(5)}^{2} = \frac{25 m}{2} T h u s, K_{5} = 25 K_{1}$
&
$U_{1} = m g (5) = 5 m g U_{5} = m g (1) = m g T h u s, U_{1} = 5 U_{5}$
Hence, $K_{5} > K_{1} & U_{1} > U_{5}$

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