The particle p is released at time t = 0 from the position r = r0 inside the smooth tube with no velocity relative to the tube, which is driven at the constant angular velocity ω0 about a vertical axis. determine the radial velocity vr, the radial position r, and the transverse velocity vθ as functions of time t. explain why the radial velocity increases with time in the absence of radial forces. plot the absolute path of the particle during the time it is inside the tube for r0 = 0.19 m, l = 1.4 m, and ω0 = 1.29 rad/s. then answer the questions using the given numbers.

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Arunner is jogging at a steady 3.6 km/hr. when the runner is 2.9 km from the finish line, a bird begins flying from the runner to the finish line at 14.4 km/hr (4 times as fast as the runner). when the bird reaches the finish line, it turns around and flies back to the runner. even though the bird is a dodo, we will assume that it occupies only one point in space, i.e., a zero-length bird. how far does the bird travel? (b) after this first encounter, the bird then turns around and flies from the runner back to the finish line, turns around again and flies back to the runner. the bird repeats the back and forth trips until the runner reaches the finish line. how far does the bird travel from the beginning? (i.e. include the distance traveled to the first encounter)

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