Question

A common flea is recorded to have jumped as high as 21 cm. Assuming that the jump is entirely in the vertical direction and that air resistance is insignificant, calculate the time it takes the flea to reach a height of 7.0 cm.

Answer 1

t = 0.12 s

Step-by-step explanation:

Applying the second equation of motion under free fall,

h = ut +
`(1)/(2)`g
`t^(2)`

where: h is the height, u is its initial velocity, t is the time taken and g is the gravitational force.

But, u = 0 m/s, h = 21 cm (0.21 m) and g = 9.8 m/
`s^(2)`. Then:

0.21 = 0 +
`(1)/(2)` x 9.8 x
`t^(2)`

0.21 = 4.9
`t^(2)`

`t^(2)` =
`(0.21)/(4.9)`

= 0.04286

⇒ t = 0.2070

= 0.21 s

The time taken for the flea to jump as high as 21 cm is 0.21 s.

The time taken for the flea to reach a height of 7.0 cm (0.07 m) can be determined as;

h = ut +
`(1)/(2)`g
`t^(2)`

0.07 = 0 +
`(1)/(2)` x 9.8 x
`t^(2)`

0.07 = 4.9
`t^(2)`

`t^(2)` =
`(0.07)/(4.9)`

= 0.01429

t = 0.1195

= 0.12 s