Question

A flea jumps into the air and lands about 8 inches away, risen to a height 130 times its own height. Assuming the flea jumped at a 45° angle with the horizontal, what must its take of speed have been? Note: convert 9.8 meters per second squared to in.²

Answer 1

The takeoff speed of the flea can be calculated using the principle of conservation of mechanical energy.

Step-by-step explanation:

To determine the takeoff speed of the flea, we can use the principle of conservation of mechanical energy. Assuming no air resistance, the initial potential energy of the flea at its maximum height is equal to its initial kinetic energy.

The potential energy of the flea at its maximum height can be calculated as 130 times its gravitational potential energy:

PE = (130 × m × g × h)

Where m is the mass of the flea, g is the acceleration due to gravity, and h is the height the flea jumps.

The initial kinetic energy of the flea can be calculated as:

KE = (0.5 × m × v^2)

Where v is the takeoff speed of the flea.

Equating the potential energy and kinetic energy, we can solve for v:

(130 × m × g × h) = (0.5 × m × v^2)

Simplifying the equation, we get:

v = sqrt ((260 × g × h))

Substituting the values of g = 9.8 m/s^2 (conversion factor to inches^2 is not required) and h = 8 inches, we can find the takeoff speed of the flea.