Question

BIO Human Energy vs. Insect Energy.
For its size, the common flea is one of the most accomplished jumpers in the animal world. A 2.0-mm-long, 0.50-mg flea can reach a height of 20 cm in a single leap. Ignoring air drag, what is the takeoff speed of such a flea?

Answer 1

Answer:

The takeoff speed of the flea is 1.98 m/s.

Explanation:

Consider upward direction as positive and downward direction as negative.

Given:

Length of the flea (L) = 2.0 mm

Mass of the flea (m) = 0.50 mg

Maximum height reached by the flea (h) = 20 cm = 0.20 m [1 cm =0.10 m]

At maximum height, velocity is 0. So, final velocity (v) = 0 m/s

Acceleration of the flea is only due to gravity (g) = -9.8 m/s² (Down)

Let the initial takeoff velocity be 'u' m/s.

We know that, from kinetic equation of motion, the final velocity is related to initial velocity, acceleration and displacement as:

$v^2=u^2+2aS$

Where, 'a' and 'S' are the acceleration and displacement of the body respectively.

As per question,

$a = g = -9.8$ m/s²

$S = h = 0.20\ m$

Plug in the given values and solve for 'u'. This gives,

$0=u^2-2\times 9.8\times 0.20\\\\u^2=3.92\\\\\sqrt{u^2}=\sqrt{3.92}\\\\u=1.98\ m/s$

Therefore, the takeoff speed of the flea is 1.98 m/s.