Carlos runs with velocity \vec{v}v →= (5.6 m/s, 29o north of east) for 10 minutes. How far to the north of his starting position does Carlos end up? (Give your answer to the nearest meter)

Students design a model roller-coaster track. they place a rubber ball at the highest point on the track and let it go. the ball rolls along the track pulled only by the force of gravity. eventually, it comes to a stop. which change to the design will result in the ball moving the greatest distance?

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)

A100-watt light bulb illuminates a solar cell. the electricity from the solar cell operates a water pump that delivers 1 watt of power. what is the efficiency of the system?