1

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?An errand of mercy: An airplane is dropping bales of hay to cattle stranded in a blizzard on the Great Plains. The pilot releases the bales at 150 m above the level ground when the plane is flying at 75 m/s in a direction 55" above the horizontal. How far in front of the cattle should the pilot release the hay so that the bales land at the point where the cattle are stranded?A web page designer creates an animation in which a dot on a computer screen has position T = [4.0 cm + (2.5 cm/s?) ?]i + (5.0cm/s) tj (a) Find the magnitude and direction of the dot's average velocity between t =0 and t = 2.0s. (b) Find the magnitude and figration of the instantaneous velocity at t = 0, t = 1.0s, and t = 2.0s. (c) Sketch the dot's trajectory from t = 0 to t = 2.0s, and show the velocities calculated in part (b)