Find the magnitude of the sum of a 10m displacement and a 5 -m displacement when the angle between them is 45o

What are two different ways you could find the value of a? explain these methods.

Your starship, the aimless wanderer, lands on the mysterious planet mongo. as chief scientist-engineer, you make the following measurements: a 2.50-kg stone thrown upward from the ground at 14.0 m/s returns to the ground in 5.70 s ; the circumference of mongo at the equator is 2.20×10^5 km ; and there is no appreciable atmosphere on mongo. (a) the starship commander, captain confusion, asks for the following information: what is the mass of mongo? (b) if the aimless wanderer goes into a circular orbit 2.20×10^4 km above the surface of mongo, how many hours will it take the ship to complete one orbit? (c) an unmanned spacecraft is in a circular orbit around the moon, observing the lunar surface from an altitude of 44.0 km . to the dismay of scientists on earth, an electrical fault causes an on-board thruster to fire, decreasing the speed of the spacecraft by 23.0 m/s . if nothing is done to correct its orbit, with what speed (in km/h) will the spacecraft crash into the lunar surface?

In the circuit, the switch s has been open for a long time and r = 125 kohm. it is then suddenly closed. (a) determine the time constant before the switch is closed. s (b) determine the time constant after the switch is closed. _ s (c) let the switch be closed at t = 0. find the current in the switch as a function of time. (use t for time. express your answer in milliamps and seconds.) i(t) =_