Measuring Height to Calculate Froghopper Jump Height

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SUMMARY

The froghopper (Philaenus spumarius) is recognized as the best jumper in the animal kingdom, capable of accelerating at 4400 m/s² over a distance of 2.0 mm. After this acceleration, it reaches a velocity of 4.19 m/s in 0.952 milliseconds. To calculate the jump height, the equation v² = v₀² + 2ay can be utilized, where 'v' is the final velocity, 'v₀' is the initial velocity, 'a' is the acceleration due to gravity, and 'y' is the height. The actual jump height achieved by the froghopper is approximately 0.7 m, indicating the significant impact of air resistance on its performance.

PREREQUISITES
  • Understanding of kinematic equations, specifically v² = v₀² + 2ay
  • Basic knowledge of acceleration and gravity
  • Familiarity with the concept of air resistance in physics
  • Ability to perform unit conversions and calculations in physics
NEXT STEPS
  • Research the effects of air resistance on jumping insects
  • Study advanced kinematic equations and their applications
  • Explore the biomechanics of insect locomotion
  • Learn about the physics of projectile motion and its relation to jump height
USEFUL FOR

Students studying physics, entomologists researching insect behavior, and anyone interested in biomechanics and the physics of motion.

parwana
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help with part b

It has been claimed that an insect called the froghopper (Philaenus spumarius) is the best jumper in the animal kingdom. This insect can accelerate at 4400 m/s2 over a distance of 2.0 mm as it straightens its specially designed "jumping legs."

I got this right

(a) Assuming a uniform acceleration, what is the velocity of the insect after it has accelerated through this short distance, and how long did it take to reach that velocity?
velocity 4.19 m/s
elapsed time .952 ms




(b) How high would the insect jump if air resistance could be ignored? Note that the actual height obtained is about 0.7 m, so air resistance is important here.

I don't know what to for part b

should I plug into the equation v^2= v0^2 + 2ax?

or what? Its driving me insane
 
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is the bug jumping verticaly?
 
Once the bug leaves the ground gravity takes over and he will start to delcelarate due to gravitational attraction. That is it cannot accelerate itself any more since it cannot push against the surface. So it will decelerate at a rate of g. Your choice of equation will therefore do just fine. But maybe you should replace the x with a y (joking).
 

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