Question

Take the magnitude of free-fall acceleration to be g. Ignore air resistance.

(a) A flea jumps straight up to a maximum height of h. What is its initial velocity as it leaves the ground?

(b) How long is the flea in the air from the time it jumps to the time it hits the ground?

Answer 1

(a)

By third kinematics law,

v^2 - u^2 = 2*a*S

here, v = final velocity at maximum height = 0

u = initial velocity = ??

a = acceleration in upward direction = -g

S = distance travel by flea = h

So, 0^2 - u^2 = 2*(-g)*h

u = sqrt(2*g*h)

(b)

By first kinematics law,

v = u + a*t

here, v = final velocity when flea reaches at maximum height 'h' = 0

from Part(a), u = sqrt(2*g*h)

a = -g

t = time taken to reach at maximum height = ??

So, t = sqrt(2*g*h)/g

t = sqrt(2*h/g)

now total time of flight of flea is given by,

T = 2*t (because given that air resistance is negligible)

So, T = 2*sqrt(2*h/g)

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