BIO The Champion Jumper of the Insect World.? The froghopper, ?Philaenus spumarius,? holds the world record for insect jumps. When leaping at an angle of 58.0° above the horizontal, some of the tiny critters have reached a maximum height of 58.7 cm above the level ground. (See ?Nature,? Vol. 424, July 31, 2003, p. 509.) (a) What was the takeoff speed for such a leap? (b) What horizontal distance did the froghopper cover for this world-record leap?
Solution 14E Step 1: 0 The angle at which the projectile fired is, = 58 . The maximum height it reached is, hmax = 58.7 cm. By the formula of maximum height for a projectile motion, V sin hmax = 2g ----------------(1) V sin 58 58.7 = 2×9.8 V sin 58 V ×0.8482 58.7 = 2×9.8 = 19.6 2 58.7×19.6 V = 0.719 = 1600 V = 1600 = 40 m/s.