Afish swimming in a horizontal plane has velocity i = (4.00 î + 1.00 ĵ) m/s at a point in the ocean where the position relative to a certain rock is i = (12.0 î − 3.60 ĵ) m. after the fish swims with constant acceleration for 15.0 s, its velocity is = (15.0 î − 6.00 ĵ) m/s.

Research the neutrino using the internet and report your findings. in a nuclear decay, the nucleus of an atom splits apart. larger particles can be detected and their masses and velocities can be recorded. explain how the existence and properties of the neutrino could be predicted using the conservation laws.

The particle in a two-dimensional well is a useful model for the motion of electrons around the indole ring (3), the conjugated cycle found in the side chain of tryptophan. we may regard indole as a rectangle with sides of length 280 pm and 450 pm, with 10 electrons in the conjugated p system. as in case study 9.1, we assume that in the ground state of the molecule each quantized level is occupied by two electrons. (a) calculate the energy of an electron in the highest occupied level. (b) calculate the frequency of radiation that can induce a transition between the highest occupied and lowest unoccupied levels. 9.27 electrons around the porphine ring (4), the conjugated macrocycle that forms the structural basis of the heme group and the chlorophylls. we may treat the group as a circular ring of radius 440 pm, with 20 electrons in the conjugated system moving along the perimeter of the ring. as in exercise 9.26, assume that in the ground state of the molecule quantized each level is occupied by two electrons. (a) calculate the energy and angular momentum of an electron in the highest occupied level. (b) calculate the frequency of radiation that can induce a transition between the highest occupied and lowest unoccupied levels.

Aplayground merry-go-round has a radius of 4.6 m and a moment of inertia of 200 kg-m2 and turns with negligible friction about a vertical axle through its center. a child applies a 26.0 n force tangentially to the edge of the merry-go-round for 15.0 seconds. if the merry-go-round is initially at rest, how much work did the child do on the merry-go-round?