A truck carrying watermelons stops suddenly at the edge of a washed-out bridge (see figure below). The sudden stop causes several watermelons to fly off the truck. One watermelon rolls over the cab of the truck and is moving with an initial speed v₁ = 16.0 m/s in the horizontal direction at the instant shown. The river bank's cross section has the shape of the bottom half of a parabola, with its vertex at the initial location of the projected watermelon and with the equation y² = 8x, where x and y are measured in meters. (The origin of the coordinate system is the initial position of the watermelon.) What are the x- and y-coordinates (in m) of the melon when it splatters on the bank? X = y = 3 3 m Vi x

The banded archerfish is a species of fish that lives in mangrove estuaries in Asia and Oceania. It has a unique and highly effective hunting strategy: it shoots an incredibly precise stream of water out of its mouth at almost ten meters per second, knocking insects and other small animals into the water from nearby branches! Pom Fbug (t) Ө = Our hero, a hungry archerfish, has spotted a big, delicious bug sitting on a branch a height ħ above the surface of the water. The archerfish can shoot its water jet at a speed of vo. The archerfish wants to knock the bug sideways off of the branch, so it decides to shoot so that its water jet is moving horizontally at the moment when it strikes the bug. The final goal of this problem is to find the horizontal distance, d, from the branch, and the angle above horizontal, 0, at which archerfish should shoot. d (a) What are the position and velocity of the water droplet as a function of time and the position and velocity of the bug as a function of…

= (e) In the figure below, a solid ball rolls smoothly from rest (starting at height H 6.0 m) until it leaves the horizontal section at the end of the track, at height h = 2.0 m. How far horizontally from point A does the ball hit the floor? H

A motorcycle daredevil plans to ride up a 2.00 m high 26.0° ramp, sail across a 10-m-wide pool filled with hungry crocodiles, and land at ground level on the other side. He has done this stunt many times and approaches it with confidence. Unfortunately, the motorcycle engine dies just as starts up the ramp. He is going 14.9 m/s at that instant, and the rolling friction of his rubber tires is not negligible. Assuming that the local acceleration due to gravity is -9.80 m/s2, calculate the landing point (in m) relative to the 10.0 m edge of the pool. (-1.0 m means he was 1.0 m short and in the pool, +1.0 m means he landed 1.0 m past the edge). The coefficient of rolling friction for rubber on ramp is 0.02.