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Fleas are great jumpers. When a flea jumps vertically, it can reach a maximum height of 18 cm. i. What is the initial velocity at its takeoff? ii. If the flea jumps at an angle of 60 degrees with respect to the ground, how far can it jump?

User Speldosa
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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.

User Pokoli
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