Pessimist Singularitarian

#8
December 29th, 2017,
07:49
Originally Posted by

**karush**
**a.** If a flea can jumps straight up to a height of **0.440m**.

what is the initial speed as it leaves the ground.

**b.** For how much time is it in the air?

ok I am sure we use this equation

$$x=x_0+v_o^t+\frac{1}{2} at^2$$

I watched another **YT** on this but it got to much complication

better just to come here

For part a), we could use conservation of energy...initially the flea has kinetic energy, and then when it reaches the apex of its jump, it has potential energy:

$ \displaystyle \frac{1}{2}mv_0^2=mgh$

Solving for $v_0$, we obtain:

$ \displaystyle v_0=\sqrt{2gh}$

For part b), we could write:

$ \displaystyle h(t)=\frac{t}{2}\left(2v_0-gt\right)$

We are interested in the non-zero root, hence:

$ \displaystyle t=\frac{2v_0}{g}=\frac{2\sqrt{2gh}}{g}=2\sqrt{\frac{2h}{g}}$