(1) [In this problem and the next i,j,k are not the local east, north up directions.] A mouse scurrying towards a cheezit on the floor of a subway car has a velocity of 3 m/s j relative to the car and the car has a velocity of -13 m/s i+ 15 m/s k relative to the local patch of the Earth's surface and the local patch of the Earth's surface has a velocity of .3563 km/s j relative to the center of the Earth. What is the speed of the mouse relative to the center of the Earth.(2) What angle does the velocity of the mouse in problem(1) relative to the center of the Earth make with the x-y plane? What angle does the projection of the velocity of the mouse in the x-y plane make with the +x direction?(3) A professor in a crowded subway car experiences a force of -2L.00X103 N k from gravity, a force of 1.00X103 N k from the floor of the car, a force of -20 N ifrom his neighbor to his right and a force of 15 N j from his neighbor behind him. The net force on the professor is the sum of these four forces. Find the magnitude and direction of the net force on the professor. (4) The acceleration of the professor in problem (3) is the net force on him divided by his mass, 102 kg. What are the M and 2 components of the acceleration of the professor in SI unis. (5) If the professor in problem (4} were initially at rest and the acceleration was constant and lasted 0.25 seconds, what would his instantaneous velocity be at the end of that time