Final answer:
The takeoff speed of a flea that can jump to a height of 18.0 cm, ignoring air resistance, is found using energy conservation principles and is calculated to be approximately 1.88 m/s.
Step-by-step explanation:
The student is asking about the takeoff speed of a flea that is able to jump to a height of 18.0 cm. To find this, we need to use the principles of kinematics and energy conservation. When a flea jumps to a certain height, we can ignore air resistance as the question suggests and use the formula derived from the conservation of energy PE = KE, where PE is the potential energy at the height of the jump, and KE is the kinetic energy at takeoff. The equation can be written as mg(h) = (1/2)mv^2, where m is the mass of the flea, g is the acceleration due to gravity (9.8 m/s^2), h is the height reached (0.18 m), and v is the takeoff speed we want to find.
To solve for v, we can rearrange the formula to v = sqrt(2gh). Plugging the values in, we get v = sqrt(2 * 9.8 m/s^2 * 0.18 m), which gives us the takeoff speed v that the flea requires to reach the height of 18.0 cm. After calculating, the takeoff speed of the flea is approximately 1.88 m/s.