Astronomers discover an exoplanet (a planet of a star other than the sun that has an orbital period of 3.41 earth years in its circular orbit around its sun, which is a star with a measured mass of 3.13 × 1030 kg. find the radius of the exoplanet\'s orbit.

Keneila is attempting to ski down a 20 m high friction free hill for the first time. she has a speed 10 m/s at the top. what is her kinetic energy when she is a the bottom, 20 m ? (a)2500 j (b)9800 j (c)12300 j (d)3100j (e)15000j

Consider an ordinary, helium-filled party balloon with a volume of 2.2 ft3. the lifting force on the balloon due to the outside air is the net resultant of the pressure distribution exerted on the exterior surface of the balloon. using this fact, we can derive archimedes’ principle, namely that the upward force on the balloon is equal to the weight of the air displaced by the balloon. assuming that the balloon is at sea level, where the air density is 0.002377 slug/ft3, calculate the maximum weight that can be lifted by the balloon. note: the molecular weight of air is 28.8 and that of helium is 4.

The image shows the positions of a car on a roller coaster track. arrange the cars in order based on their gravitational potential energy. begin with the lowest potential energy and end with the highest.