In order to increase his gravitational potential energy by an amount equal to his kinetic energy at full speed, how high would such a sprinter need to climb

Aplanet of mass m 6.75 x 1024 kg is orbiting in a circular path a star of mass m 2.75 x 1029 kg. the radius of the orbit is r 8.05 x107 km. what is the orbital period (in earth days) of the planet tplanet?

"an open tank has the shape of a right circular cone. the tank is 6 feet across the top and 5 feet high. how much work is done in emptying the tank by pumping the water over the top edge? note: the density of water is 62.4 lbs per cubic foot."

Ahot-air balloonist, rising vertically with a constant speed of 5.00 m/s releases a sandbag at the instant the balloon is 40.0 m above the ground. after it is released, the sandbag encounters no appreciable air drag. compute the velocity of the sandbag at 0.250 s after its release.