Question

How much time is it in the air?

a) If a flea can jump straight up to a height of 0.520 m, what is its initial speed as it leaves the ground?
b) For how much time is it in the air?

Answer 1

`3.194\ m/s` & `0.6512 \ s`

Explanation:

If `u` is the initial upward speed of flea to reach a maximum vertical height `h=0.52\ m` against the gravity where its velocity becomes zero i.e. `v=0`

Now, from third equation of motion

`v^2=u^2+2as`

For motion against gravity

`v^2=u^2-2gh`

`0^2=u^2-2(9.81)(0.52)`

`u=\sqrt{2\cdot 9.81\cdot 0.52}`

`=3.194\ m/s`

The taken `t` by flea to reach to maximum height where final velocity `v=0`, is given from first equation of motion

`v=u+a t`

For motion against gravity

`v=u-g t`

`0=3.194-9.81t`

`t=0.3256\ s`

hence, total time when flea remains in the air

`=2\times 0.3256`

`=0.6512\ s`