Chapter 5.1, Problem 5.2P

Given the vectors shown, sketch ū + v, ū–v, and 2ū . 3. Write each vector below as a combination of the vectors ū and v from question #3. 6.

angle 0 given by the expression a tane 3. A particle is projected vertically upward from the surface of the rotating earth at colatitude (polar angle) 0. It rises to a height h(« R) and then falls back to the surface. Show that it 8 1/2 strikes the ground at distance o sino(2h/g)* to the west of the initial position. What 3 is its westward displacement at its maximum height?

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…