The tape is now wound back into the drum at angular rate ω(t). with what velocity will the end of the tape move? (note that our drawing specifies that a positive derivative of x(t) implies motion away from the drum. be careful with your signs! the fact that the tape is being wound back into the drum implies that ω(t)< 0, and for the end of the tape to move closer to the drum, it must be the case that v(t)< 0.

Anew obstacle course is home to several new types of challenging obstacles. one such obstacle is traversing a 15-stair staircase. to make it more challenging, the stairs are not uniformly spaced. rather, the vertical space between consecutive stairs for the first 10 stairs is 113 feet and the vertical space for the last 5 stairs is 134 feet. what is the total vertical distance traveled ascending and descending the entire 15-stair staircase?