Jessica and matthew are running toward the point p along the straight paths that make a fixed angle of θ. suppose that matthew runs with velocity va meters per second and jessica with velocity vb meters per second. assume that θ = π/3. use the chain rule to determine the rate at which the distance f between matthew and jessica is changing when x = 40, y = 30, va = 4 m/s, and vb = 3 m/s.

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.