Question

When jumping, a flea accelerates at an astounding 1000 m/s2, but over only the very short distance of 0.50 mm. If a flea jumps straight up, and if air resistance is neglected (a rather poor approximation in this situation), how high does the flea go?

Answer 1

The flea will move high to a height of 0.05 meters.

Step-by-step explanation:

Given that,

Acceleration of the flea,
`a=1000\ m/s^2`

Distance, d = 0.5 mm = 0.0005 m

Let u and v are the initial and final velocity of the flea. Using equation of motion as :

`v^2-u^2=2ad`

`v^2-u^2=2* 1000* 0.0005`

`v^2-u^2=1`..........(1)

Using conservation of energy, we get :

`(1)/(2)mu^2=(1)/(2)mv^2+mgh`

`(1)/(2)u^2=(1)/(2)v^2+(-g)h`

`(1)/(2)u^2=(1)/(2)v^2-gh`

`(1)/(2g)(u^2-v^2)=-h`

`h=(1)/(2g)`

`h=(1)/(2* 9.8)`

h = 0.05 meters

So, the flea will move high to a height of 0.05 meters. Hence, this is the required solution.