(1) Identical twins Kate and Karen are rowing their boat on a hot Summer afternoon when they decide to go for a swim. Kate, whose mass is 40 kilograms, jumps off the front of the boat at a speed of 3.00 m/sec. Karen jumps off the back at a speed of 4.00 m/sec. If the 70 kilogram rowboat is moving at 1.00 m/s before the girls jump, what is the speed of the rowboat after the girls jump? m/sec J) A 0.10 kilogram piece of modeling clay is tossed at a motionless 0.10 kilogram block of wood and sticks. The block slides across a frictionless table at 13.7 m/sec. LAt what speed was the clay tossed? m/sec Enter a number. II. The clay is replaced with a "bouncy" ball tossed with the same speed. The bouncy ball rebounds from the wooden block at the same speed as in part I. What effect does this have on the wooden block? O There is no momentum difference upon impact with the block between the clay and bouncy ball since they are thrown at the same speed and have the same mass. O The wooden block…

The carbon isotope 14C is used for carbon dating of objects.  A  14C nucleus can change into a different kind of element, a neighbor on the periodic table with lower mass, by emitting a beta particle – an electron or positron – plus a neutrino or an anti-neutrino.  Consider the scenario where 14C ( mass of 2.34 x 10 -26) decays by emitting an electron and anti neutrino.  The electron has a mass of 9.11x 10-31 kg and a speed of 5.5 x107  m/s.  While the anti neutrino has  a momentum of 8.5x10-24 kg-m/s.  If the electron and anti neutrino are emitted at right angles from each other, calculate the recoil speed of the nucleus.