The coordinates of a particle in the metric xy-plane are differentiable functions of time t with startfraction dx over dt endfraction equalsnegative 6 startfraction m over sec endfraction and startfraction dy over dt endfraction equalsnegative 4 startfraction m over sec endfraction . how fast is the particle's distance from the origin changing as it passes through the point (12,5)?

Aball is thrown from the top of a building with an initial velocity of 21.9 m/s straight upward, at an initial height of 51.6 m above the ground. the ball just misses the edge of the roof on its way down, as shown in the figure. (a) determine the time needed for the ball to reach its maximum height. (b) determine the maximum height. (c) determine the time needed for the ball to return to the height from which it was thrown, and the velocity of the ball at that instant. (d) determine the time needed for the ball to reach the ground. (e) determine the velocity and position of the ball at t = 5.35 s.