Serway & Jewett — Motion in One Dimension: Problem 35

The froghopper Philaenus spumarius is supposedly the best jumper in the animal kingdom. To start a jump, this insect can accelerate at \(4.00\text{ km/s}^2\) over a distance of \(2.00\text{ mm}\) as it straightens its specially adapted “jumping legs.” Assume the acceleration is constant. (a) Find the upward velocity with which the insect takes off. (b) In what time interval does it reach this velocity? (c) How high would the insect jump if air resistance were negligible? The actual height it reaches is about \(70\text{ cm}\), so air resistance must be a noticeable force on the leaping froghopper.