A helicopter flies with an airspeed of 42.5 m/s [W]. If the wind is traveling with a velocity of 25.0 m/s [E30°S] relative to the ground then determine the velocity of the helicopter relative to the ground. Use the data from the question to determine the velocity components for the helicopter's speed relative to the air and the wind's speed relative to the ground. Use your velocity components from part (a) and determine the resultant velocity for each component. (In other words, determine the resultant horizontal component for the helicopter's ground speed and the resultant vertical component for the helicopter's ground speed). Using your data, determine the resultant velocity of the helicopter relative to the ground.

The ultracentrifuge is an important tool for separating and analyzing proteins. because of the enormous centripetal accelerations, the centrifuge must be carefully balanced, with each sample matched by a sample of identical mass on the opposite side. any difference in the masses of opposing samples creates a net force on the shaft of the rotor, potentially leading to a catastrophic failure of the apparatus. suppose a scientist makes a slight error in sample preparation and one sample has a mass 10 mg larger than the opposing sample. if the samples are 12 cm from the axis of the rotor and the ultracentrifuge spins at 70,000 rpm, what is the magnitude of the net force on the rotor due to the unbalanced samples? ( be thorough on your answer)