Aspaceship is projected vertically upward from the earth's surface with an initial speed of 7.51 km/s, but unfortunately does not have a great enough speed to escape earth's gravity. what maximum height does the spaceship reach (in m)? ignore air resistance.

After the near spacecraft passed mathilde, on several occasions rocket propellant was expelled to adjust the spacecraft's momentum in order to follow a path that would approach the asteroid eros, the final destination for the mission. after getting close to eros, further small adjustments made the momentum just right to give a circular orbit of radius 45 km (45 × 10^3 m) around the asteroid. so much propellant had been used that the final mass of the spacecraft while in circular orbit around eros was only 545 kg. the spacecraft took 1.04 days to make one complete circular orbit around eros. calculate what the mass of eros must be.

Air is held within a frictionless piston-cylinder container, which is oriented vertically. the mass of the piston is 0.45 kg and the cross-sectional area is 0.0030 m2. initially (state 1) the pressure of the gas is sufficient to support the weight of the piston as well as the force exerted by the atmospheric pressure ( 101.32 kpa). the volume occupied by the air within the cylinder in state 1 is 1.00 liter. one end of a spring (with spring constant k = 1000 n/m) is attached to the top of the piston, while the other end of the spring is attached to a stage that can move vertically. initially the spring is undeflected and therefore exerts no force. then the stage is then moved quasistatically downward a distance of 10.0 cm, at which point the system reaches state 2. the piston-cylinder is not insulated; rather it remains in diathermal contact with the surroundings, which are at a constant temperature of 300 k. what is the change of pressure within the container?

According to the tide table below what time of day will the highest tide occur?