Emilio tries to jump to a nearby dock from a canoe that is floating in the water. instead of landing on the dock, he falls into the water beside the canoe. use newtons third law to explain why this happened. hint: first identify the action-reaction pair in this example.

Suppose a wheel with a tire mounted on it is rotating at the constant rate of 2.15 times a second. a tack is stuck in the tire at a distance of 0.373 m from the rotation axis. noting that for every rotation the tack travels one circumference (a) find the tack's tangential speed. (b) what is the tacks radial acceleration?

Consider a double atwood machine constructed as follows: a mass 4m is suspended from a string that passes over a massless pulley on frictionless bearings. the other end of this string supports a second similar pulley, over which passes a second string supporting a mass of 3m at one end and m at the other. using two suitable generalized coordinates, set up the lagrangian and use the lagrange equations to find the acceleration of the mass 4m when the system is released. explain why the top pulley rotates even though it carries equal weights on each side.

Two students, each riding bicycles, start from the same apartment building and ride to the same building on campus, but each takes a different route. the first student rides 1100 m due east and then turns due north and travels another 1430 m before arriving at the destination. the second student heads due north for 1930 m and then turns and heads directly toward the destination. at the turning point, how far is the second student from the destination?