Final answer:
The initial velocity of a flea during takeoff is calculated using kinematic equations for vertical motion, considering gravity. For jumping at an angle, projectile motion equations are used, and it is noted that a 60-degree launch angle is not optimal for maximum distance.
Step-by-step explanation:
The question asks about determining the initial velocity of a flea during its takeoff when jumping to a certain height, and how far it can jump at a 60-degree angle. To calculate the initial velocity at takeoff, we can use the kinematic equation for vertical motion under constant acceleration due to gravity (9.81 m/s2):
v2 = u2 + 2as, where 'v' is the final velocity (0 m/s at the maximum height), 'u' is the initial velocity which we want to find, 'a' is the acceleration (gravitational, which is -9.81 m/s2 when upwards is taken as positive), and 's' is the displacement (18 cm or 0.18 m).
For the second part, to find the horizontal distance jumped by the flea at a 60-degree angle, we use the projectile motion equations and consider both vertical and horizontal components of the initial velocity. Since the maximum range for projectile motion is reached at a 45-degree angle, jumping at a 60-degree angle would not provide the maximum distance. Hence, less distance would be covered compared to the maximum range.