Adam the ant gets a running start and leaps with speed 310 cm/s and lands on top of a 20 cm tall...

Question:

Adam the ant gets a running start and leaps with speed 310 cm/s and lands on top of a 20 cm tall anthill. What is his speed as he lands?

Kinetic and Potential Energy:

The energy of the object due to its motion is known as the kinetic energy of the object. And the energy due to the virtue of height is known as the Potential energy.

Given data

• Initial speed {eq}(u) = 310 \ cm/s (u) = 3.1 \ m/s {/eq}
• Height of the hill {eq}(h) = 0.2 \ m {/eq}

The initial energy of Adam would be only kinetic energy, therefore

{eq}E_{1} = \dfrac{1}{2}mu^{2} {/eq}

where

• m is the mass of Adam

Now, the energy at the hill would be both kinetic as well as the potential, therefore

{eq}E_{2} = mgh + \dfrac{1}{2}mv^{2} {/eq}

where

• v is the speed at the hill

Now, from the energy conservation

{eq}E_{1} = E_{2} \\ \dfrac{1}{2}mu^{2} = mgh + \dfrac{1}{2}mv^{2} \\ (0.5*3.1^{2}) = (9.8*0.2) + (0.5v^{2}) \\ v = 2.385 \ m/s {/eq}