Question

A flea jumps straight up to a maximum height of 0.420 m . what is its initial velocity v0 as it leaves the ground? how long is the flea in the air from the time it jumps to the time it hits the ground?

Answer 1

Initial velocity = $\(v_0\)$

acceleration in the downward direction = -9.8 $\(\frac {m}{s^2}\)$

Final velocity at the highest point = 0

Maximum height reached = 0.420 m

Now, Using third equation of motion:

$\(v^2 = {v_0}^{2} + 2aH$

$\(0^2 = {v_0}^{2} - 2 \times 9.8 \times 0.420$

$\({v_0}^{2} = 2 \times 9.8 \times 0.420\)$

$\(v_0 = 2.869 \frac {m}{s}\)$

Velocity with which the flea jumps = $\(2.869 \frac {m}{s}\)$

Let the time for half journey be t.

$\(v = v_0 + at\)$

$\( t = \frac{2.869}{9.8}\)$

t = 0.2927 s

Total time flea stayed in air = $\( 2 \times 0.2927\)$

T = 0.5854 s