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Derive Equations 1 and 2
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- Find the magnitude and direction of A(-6,4)B(-9,-3).A river of width' a' with straight parallel banks flows due north with speed u. The points O and A are on opposite banks and A is due east of O. Coordinate axes Ox and Oy are taken in the east and north directions respectively. A boat, whose speed is v relative to water, starts from O and crosses the river. If the boat is steered due east and u varies with x as : u = r(a – x) - 2). Find: equation of trajectory of the boatConsider the case of projectile motion under gravity in two dimensions. Find the equation of motion in both Cartesian and polar coordinates.
- A stone is thrown from a rooftop at time t = 0 seconds. Its %3D position at timet is given by F(t) = (7t,-31, 19.6 – 4.91). %3D The origin is at the base of the building, which is standing on flat ground. Distance is measured in meters. The vector i points east, j points north, and k points up. (a) How high is the rooftop? meters. (b) When does the stone hit the ground? seconds. (c) At what point (in R') does the stone hit the ground? (in meters) (d) How fast is the stone moving when it hits the ground? (in meters per second)At the beginning of a 3 hour trip you're traveling due north at 192 km/hour. at the end, you are traveling 240km/hour at 45° west of north. a) Draw the initial and final velocity vectors b) find ΔvThe force P of magnitude 50 kN is acting at 215° from the x-axis. Find the components of P in v 157° from x, .and u negative 69° from x